® 
1 Abstract
There has already 2 years passed by while Binary.com-is-Rebranding-to-Deriv.com, Here I summarized some previous research papers in Binary.com → Deriv.com and continue from this high-frequency-trading.
if(!suppressPackageStartupMessages(require('BBmisc'))) {
install.packages('BBmisc', dependencies = TRUE, INSTALL_opts = '--no-lock')
}
suppressPackageStartupMessages(require('BBmisc'))
# suppressPackageStartupMessages(require('rmsfuns'))
pkgs <- c('devtools', 'knitr', 'kableExtra', 'tint', 'dygraphs',
'devtools','readr', 'lubridate', 'data.table', 'reprex',
'feather', 'purrr', 'quantmod', 'tidyquant', 'plotly',
'tibbletime', 'furrr', 'flyingfox', 'tidyr', 'jsonlite',
'timetk', 'plyr', 'dplyr', 'stringr', 'magrittr', 'tdplyr',
'tidyverse', 'memoise', 'htmltools', 'formattable',
'dash', 'dashCoreComponents', 'dashHtmlComponents', ##https://dashr.plotly.com
'zoo', 'forecast', 'seasonal', 'seasonalview', 'rjson',
'rugarch', 'rmgarch', 'mfGARCH', 'sparklyr', 'jcolors',
'microbenchmark', 'dendextend', 'lhmetools', 'ggthemr',
'stringr', 'pacman', 'profmem', 'DescTools', 'ggthemes',
'htmltools', 'echarts4r', 'viridis', 'hrbrthemes')
# https://github.com/mpiktas/midasr
# https://github.com/onnokleen/mfGARCH
# devtools::install_github("business-science/tibbletime")
# devtools::install_github("DavisVaughan/furrr")
suppressAll(lib(pkgs))
# load_pkg(pkgs)
funs <- c('uv_fx.R', 'opt_arma.R', 'multi_seasons.R',
'filterFX.R', 'filter_spec.R', 'mv_fx.R',
'task_progress.R', 'read_umodels.R', 'convertOHLC.R')
l_ply(funs, function(x) source(paste0('./function/', x)))
# spark_install()
# if(FALSE) {
# Not run due to side-effects
# spark_home_set()
# }
# sc <- spark_connect(master = 'local')
#spark_install()
#sc <- spark_connect(master = 'local')
.cl = FALSE
Sys.setenv(TZ = 'Asia/Tokyo')
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, knitr.table.format = 'html')#, digits.secs = 6)
rm(pkgs, funs)2 Introduction
By refer to GARCH模型中的ARIMA(p,d,q)参数最优化 and binary.com Interview Question I - Comparison of Univariate GARCH Models, we know Fractional Intergrated GJR-GARCH is the best fit model. This paper we compare the MIDAS, GARCH-MIDAS and Levy Process models. Here I also test another high frequency trading model mcmcsGARCH. These paper might consider as comparison interday trading before start the high frequency trading via Real Time FXCM.
High Frequency Financial Time Series Prediction - Machine Learning Approach introduce multilayer modelling for high-frequency-trading. binary.com Interview Question I - Tick-Data-HiLo For Daily Trading (Blooper) tried to use Hi-Lo daily dataset for modelling but failed. The paper recommend to use complete itraday dataset.
I noticed that buying early in the morning, around 5am eastern time, tends to give lower prices and selling around 10pm eastern time gives you the highest prices. The wording is weird but i want to know your opinions on how time of day affects the bitcoin trading market. Thank you.
Source : Time of day affects trading prices
From above quotes, we can know the seasonality of price trend daily, weekly, monthly or annually etc. MIDAS and mcsGARCH are the models designate for high frequency trading.
A Comparison of GARCH-class Models and MIDAS Regression with Application in Volatility Prediction and Value at Risk Estimation compares GARCH, eGARCH and MIDAS 3 models with normal and student distribution with matrix. The author concludes that the MIDAS model is the most accurate in volatility prediction but there is inconclusive for VaR 1% and 5%.
Note that there does not seem to be an option to use SARMA models in the “rugarch” package, so you will have to let the “S” part go. But if there is a seasonal pattern (and that is quite likely when it comes to tourist arrivals), you will have to account for it somehow. Consider using exogenous seasonal variables (dummies or Fourier terms) in the conditional mean model via the argument external.regressors inside the argument mean.model in function ugarchspec. Alternatively, note that a SARMA model corresponds to a restricted ARMA model. An approximation of SARMA could thus be an ARMA with the appropriate lag order but without the SARMA-specific parameter restrictions (since those might not be available in “rugarch”).
The quotes above describe about the seasonal factors onto the model which is similar with MIDAS model, kindly refer to Fitting ARIMA-GARCH model using “rugarch” package.
3 Data
3.1 Tick Data
3.1.1 Get Data
Due to the dataset gather via getSymbols('JPY=X', src='av', api.key=api, periodicity='intraday') is tidied but only 100 observations. Moreover I cannot select the time period from few years ago, therefore here I omit it and use the intraday data gather from real-time-fxcm/data/USDJPY/ from Y2015W1 to Y2018W27, due to the dataset is tick-data-base and more than 1 million observation per file (per week) and there has 4 years dataset where. Here I need to backtest day-by-day. There will be spent a long time to do.
- Chapter 7 Importing Financial Data from the Internet introduce few packages where provides api service.
- High Frequency Data Price (Sample) is an example for intraday high-frequency-trading.
cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 'CNY=X', 'JPY=X')
names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')
# names(cr_code) <- c('USDAUD', 'USDEUR', 'USDGBP', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')
dtr <- str_extract_all(getwd(), '.*/', '')[1]
dtr1 <- paste0(dtr, 'real-time-fxcm/data/')
## Read presaved FXCM data.
# mbase <- sapply(names(cr_code), function(x) readRDS(paste0('./data/', x, '.rds')) %>% na.omit)
fls <- sapply(names(cr_code), function(x) {
dtr1 <- paste0(dtr1, x)
list.files(dtr1, pattern = '^Y[0-9]{4}W[0-9]{1,2}.rds$') %>%
str_replace_all('.rds', '')
})
fls[lengths(fls) == 0] <- NA_character_
fls[is.na(fls)] <- NULL
# AUDUSD <- sapply(fls[[1]], read_rds)
# EURUSD <- sapply(fls[[2]], read_rds)
# GBPUSD <- sapply(fls[[3]], read_rds)
# USDCHF <- sapply(fls[[4]], read_rds)
# USDCAD <- sapply(fls[[5]], read_rds)
# USDCNY <- sapply(fls[[6]], read_rds)
# mbase <- llply(as.list(fls[[7]]), read_rds) #185 files where 1 files contains 1 million observation.
## Here I take USDJPY as example...
dtr1s <- paste0(dtr1, names(fls[length(fls)]))
fs <- list.files(dtr1s, pattern = '^Y[0-9]{4}W[0-9]{1,2}.rds$') %>%
str_replace_all('.rds', '')
# eval(parse(text = paste0(fs, "<- readRDS('", fls[[7]], "') %>% as_tibble")))
t.unit <- c('seconds', 'minutes', 'hours', 'days', 'weeks', 'months', 'quarters', 'quarters')
## https://www.alphavantage.co/
## https://www.alphavantage.co/support/#api-key
# api = 'UL7EPVVEGDVC3TXC'
# getSymbols('JPY=X', src='av', api.key=api, periodicity='intraday')binary.com Interview Question I - Multivariate GARCH Models concludes that the multivariate will be more accurate but due to save time, here I only use univariate for models comparison.
Due to high volume of dataset, here I only use USDJPY since the variance is higher than the rest of currencies.
## Read raw dataset.
#Y2015W1 <- read_rds(paste0(dtr1, '/', fls[[7]][1], '.rds')) %>% as_tibble
eval(parse(text = paste0(fs[1], "<- readRDS('", dtr1, "/",
names(fls[length(fls)]), '/', fls[length(fls)][[1]][1],
".rds') %>% as_tibble")))
## raw dataset
Y2015W1## # A tibble: 1,775,999 x 3
## DateTime Bid Ask
## <fct> <dbl> <dbl>
## 1 01/04/2015 22:00:00.165 120. 121.
## 2 01/04/2015 22:00:00.197 120. 121.
## 3 01/04/2015 22:00:00.401 120. 121.
## 4 01/04/2015 22:00:00.712 120. 121.
## 5 01/04/2015 22:00:00.742 120. 121.
## 6 01/04/2015 22:00:00.786 120. 121.
## 7 01/04/2015 22:00:00.920 120. 121.
## 8 01/04/2015 22:00:00.926 120. 121.
## 9 01/04/2015 22:00:01.253 120. 121.
## 10 01/04/2015 22:00:01.259 120. 121.
## # ... with 1,775,989 more rowsAbove table shows the raw tick-dataset (shows price fluctuation in mili-seconds). As we know that the variance in unit mili-second is almost 0. Therefore I refer to High Frequency GARCH: The multiplicative component GARCH (mcsGARCH) model and use 1 minute as 1 time unit, convert from univariate ask and univariate bid to be OHLC dataset.
3.1.2 Tidy Data
For example, the
taylordata set from theforecastpackage contains half-hourly electricity demand data from England and Wales over about 3 months in 2000. It was defined astaylor <- msts(x, seasonal.periods=c(48,336).
Source Seasonal periods
A Review of Literature on Time Zone Difference and Trade study about trading across timezone and different country, if the timezone difference will affect the trading.
I would like to use R for time series analysis. I want to make a time-series model and use functions from the packages timeDate and forecast. I have intraday data in the CET time zone (15 minutes data, 4 data points per hour). On March 31st daylight savings time is implemented and I am missing 4 data points of the 96 that I usually have. On October 28th I have 4 data points too many as time is switched back. For my time series model I always need 96 data points, as otherwise the intraday seasonality gets messed up. Do you have any experiences with this? Do you know an R function or a package that would be of help to automat such data handling - something elegant? Thank you!
I had a similar problem with hydrological data from a sensor. My timestamps were in UTC+1 (CET) and did not switch to daylight saving time (UTC+2, CEST). As I didn’t want my data to be one hour off (which would be the case if UTC were used) I took the %z conversion specification of strptime. In ?strptime you’ll find:
%zSigned offset in hours and minutes from UTC, so -0800 is 8 hours behind UTC. For example: In 2012, the switch from Standard Time to DST occured on 2012-03-25, so there is no 02:00 on this day. If you try to convert “2012-03-25 02:00:00” to a POSIXct-Object,
## https://stackoverflow.com/questions/29202021/r-how-to-extract-dates-from-a-time-series
getTStime <- function(ats){
start <- start(ats)
end <- end(ats)
time <- list()
time[[1]] <- start
m <- 2
while(!(identical(start, end))){
start[2] <- start[2] + 1
if (start[2]==1441){ #mins per day
start[1] <- start[1] + 1
start[2] <- 1
}
time[[m]] <- start
m <- m + 1
}
return(time)
}
## https://stackoverflow.com/questions/13865172/handling-data-on-the-days-when-we-switch-to-daylight-savings-time-and-back-in-r
#> as.POSIXct("2012-03-25 02:00:00", tz="Europe/Vienna")
#[1] "2012-03-25 CET"
#
## you don't get an error or a warning, you just get date without the time (this behavior is documented).
## Using `format = "%z"` gives the desired result:
#
#> as.POSIXct("2012-03-25 02:00:00 +0100", format="%F %T %z", tz="Europe/Vienna")
#[1] "2012-03-25 03:00:00 CEST"
## function
as.POSIXct.no.dst <- function (
x, tz = '', format='%Y-%m-%d %H:%M', offset='+0100', ...) {
x <- paste(x, offset)
format <- paste(format, '%z')
res <- as.POSIXct(x, tz, format=format, ...)
return(res)
}Source : Handling data on the days when we switch to daylight savings time and back in R
Why is this xts frequency always 1? talk about the frequency of xts dataset and we need to use zoo to convert it.
So far, we have considered relatively simple seasonal patterns such as quarterly and monthly data. However, higher frequency time series often exhibit more complicated seasonal patterns. For example, daily data may have a weekly pattern as well as an annual pattern. Hourly data usually has three types of seasonality: a daily pattern, a weekly pattern, and an annual pattern. Even weekly data can be challenging to forecast as it typically has an annual pattern with seasonal period of
365.25/7≈52.179on average. … The top panel of Figure 11.1 shows the number of retail banking call arrivals per 5-minute interval between 7:00am and 9:05pm each weekday over a 33 week period. The bottom panel shows the first three weeks of the same time series. There is a strong daily seasonal pattern with frequency 169 (there are 169 5-minute intervals per day), and a weak weekly seasonal pattern with frequency169 × 5 = 845. (Call volumes on Mondays tend to be higher than the rest of the week.) If a longer series of data were available, we may also have observed an annual seasonal pattern.
Source : 11.1 Complex seasonality
## Convert the univariate price to be OHLC price in `minutes` unit.
Y2015W1_min1 <- Y2015W1 %>%
convertOHLC(combine = TRUE, trade = FALSE, .unit = t.unit[2]) %>%
bind_rows #combined `ask/bid` price
Y2015W1_min1## # A tibble: 7,200 x 9
## index BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-05 00:01:00 120. 121. 120. 121. 121. 121. 121.
## 2 2015-01-05 00:02:00 121. 121. 120. 121. 121. 121. 121.
## 3 2015-01-05 00:03:00 121. 121. 121. 121. 121. 121. 121.
## 4 2015-01-05 00:04:00 121. 121. 121. 121. 121. 121. 121.
## 5 2015-01-05 00:05:00 121. 121. 120. 121. 121. 121. 121.
## 6 2015-01-05 00:06:00 121. 121. 120. 120. 121. 121. 121.
## 7 2015-01-05 00:07:00 120. 121. 120. 121. 121. 121. 120.
## 8 2015-01-05 00:08:00 121. 121. 121. 121. 121. 121. 121.
## 9 2015-01-05 00:09:00 121. 121. 121. 121. 121. 121. 121.
## 10 2015-01-05 00:10:00 121. 121. 121. 121. 121. 121. 121.
## # ... with 7,190 more rows, and 1 more variable: AskClose <dbl>#suppressWarnings(Y2015W1 <- tbl %>%
# dplyr::select(date, close) %>% tk_xts %>%
# auto.arima(seasonal = FALSE))
## Count the observation in order to model seasonal frequency model.
Y2015W1_min1 %>%
dplyr::select(index) %>%
ddply(.(date(index)), summarise, n = length(index)) %>%
as_tibble## # A tibble: 6 x 2
## `date(index)` n
## <date> <int>
## 1 2015-01-05 1439
## 2 2015-01-06 1440
## 3 2015-01-07 1440
## 4 2015-01-08 1440
## 5 2015-01-09 1440
## 6 2015-01-10 1Kindly refer to section Seasonal Data or Seasonal periods to know the seasonality dataset. High Frequency GARCH: The multiplicative component GARCH (mcsGARCH) model use the dataset start from 00:01:00 but not 00:00:00, therefore above dataset shows the last observation will be the start of next day.
# tsz <- llply(fls[[7]], function(x) {
# y <- read_rds(x) %>%
# convertOHLC(combine = TRUE, trade = FALSE, .unit = t.unit[2]) %>%
# bind_rows %>%
# dplyr::filter(index == head(index, 1) |
# index == tail(index, 1)) %>%
# mutate(diff = difftime(index, lag(index, 1), units = 'mins'))
# }) %>% bind_rows %>% as_tibble %>% arrange(index)
# saveRDS(tsz, 'C:/Users/scibr/Documents/GitHub/scibrokes/real-time-fxcm/data/USDJPY/tsz.rds')
## The daylight saving convertion in not tally.
tsz <- read_rds(paste0(dtr1s, '/tsz.rds')) %>%
dplyr::filter(index >= ymd_hms('2015-01-05 00:00:00', tz = 'Europe/Athens'))
tsz## # A tibble: 368 x 10
## index AskOpen AskHigh AskLow AskClose BidOpen BidHigh BidLow
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-05 00:01:00 121. 121. 121. 121. 120. 121. 120.
## 2 2015-01-10 00:00:00 119. 119. 119. 119. 118. 118. 118.
## 3 2015-01-12 00:01:00 118. 118. 118. 118. 118. 118. 118.
## 4 2015-01-16 23:57:00 117. 118. 117. 118. 117. 118. 117.
## 5 2015-01-19 00:01:00 117. 118. 117. 117. 117. 117. 117.
## 6 2015-01-23 23:59:00 118. 118. 118. 118. 118. 118. 118.
## 7 2015-01-26 00:01:00 118. 118. 118. 118. 118. 118. 117.
## 8 2015-01-30 23:59:00 118. 118. 118. 118. 117. 118. 117.
## 9 2015-02-02 00:01:00 117. 117. 117. 117. 117. 117. 117.
## 10 2015-02-07 00:00:00 119. 119. 119. 119. 119. 119. 119.
## # ... with 358 more rows, and 2 more variables: BidClose <dbl>, diff <drtn>## count the frequency of weekly observation.
tsz %>% dplyr::count(diff) %>%
kable(caption = 'Count data point') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| diff | n |
|---|---|
| 1228 mins | 1 |
| 1276 mins | 1 |
| 1657 mins | 1 |
| 2407 mins | 1 |
| 2449 mins | 1 |
| 2650 mins | 1 |
| 2834 mins | 1 |
| 3777 mins | 1 |
| 5251 mins | 1 |
| 5395 mins | 1 |
| 5495 mins | 1 |
| 5521 mins | 1 |
| 5522 mins | 1 |
| 5620 mins | 1 |
| 5638 mins | 2 |
| 5763 mins | 2 |
| 6355 mins | 1 |
| 6831 mins | 1 |
| 6896 mins | 1 |
| 7180 mins | 1 |
| 7181 mins | 1 |
| 7187 mins | 1 |
| 7190 mins | 1 |
| 7192 mins | 1 |
| 7193 mins | 1 |
| 7194 mins | 7 |
| 7195 mins | 8 |
| 7196 mins | 9 |
| 7197 mins | 8 |
| 7198 mins | 41 |
| 7199 mins | 84 |
| NA mins | 184 |
## missing observation.
tsz %>% dplyr::filter(diff <= 6000)## # A tibble: 18 x 10
## index AskOpen AskHigh AskLow AskClose BidOpen BidHigh BidLow
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-12-24 20:02:00 120. 120. 120. 120. 120. 120. 120.
## 2 2015-12-31 20:03:00 120. 120. 120. 120. 120. 120. 120.
## 3 2016-02-03 14:58:00 119. 119. 119. 119. 119. 119. 119.
## 4 2016-04-14 15:34:00 109. 109. 109. 109. 109. 109. 109.
## 5 2016-04-19 23:15:00 109. 109. 109. 109. 109. 109. 109.
## 6 2016-05-03 16:08:00 106. 106. 106. 106. 106. 106. 106.
## 7 2016-11-17 21:41:00 110. 110. 110. 110. 110. 110. 110.
## 8 2016-12-30 23:59:00 117. 117. 117. 117. 117. 117. 117.
## 9 2017-01-06 23:59:00 117. 117. 117. 117. 117. 117. 117.
## 10 2017-04-17 20:31:00 109. 109. 109. 109. 109. 109. 109.
## 11 2017-04-25 16:53:00 111. 111. 111. 111. 111. 111. 111.
## 12 2017-05-15 21:18:00 114. 114. 114. 114. 114. 114. 114.
## 13 2017-05-23 20:12:00 112. 112. 112. 112. 112. 112. 112.
## 14 2017-06-29 19:37:00 112. 112. 112. 112. 112. 112. 112.
## 15 2017-08-08 03:39:00 111. 111. 111. 111. 111. 111. 111.
## 16 2017-12-29 23:58:00 113. 113. 113. 113. 113. 113. 113.
## 17 2018-01-06 01:00:00 113. 113. 113. 113. 113. 113. 113.
## 18 2018-01-06 01:00:00 113. 113. 113. 113. 113. 113. 113.
## # ... with 2 more variables: BidClose <dbl>, diff <drtn>## https://stackoverflow.com/questions/34454947/why-is-this-xts-frequency-always-1
## https://www.stat.berkeley.edu/~s133/dates.html
## https://stackoverflow.com/questions/45070078/convert-forecast-time-produced-by-arima-into-standard-date-time
#How to extract below index to datetime
#Y2015W1 %>% tk_ts(end = c(1440, 7200), frequency = 1440) %>% attributes %>% .$index %>% as.POSIXct(tz = 'UTC', origin = '1970-01-01') %>% force_tz(tz = 'Europe/Athens')
Y2015W1_min1 %>%
tk_ts(end = c(3, 7200), frequency = 1440) %>%
.[,1:ncol(.)] %>%
head #1440 * 5 = 7200## Time Series:
## Start = c(3, 1)
## End = c(3, 6)
## Frequency = 1440
## BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow AskClose
## 3.000000 120.474 120.542 120.442 120.502 120.534 120.638 120.520 120.608
## 3.000694 120.524 120.570 120.484 120.538 120.592 120.671 120.566 120.610
## 3.001389 120.568 120.588 120.533 120.568 120.624 120.678 120.588 120.612
## 3.002083 120.570 120.606 120.508 120.539 120.614 120.708 120.566 120.668
## 3.002778 120.544 120.594 120.472 120.576 120.668 120.714 120.506 120.598
## 3.003472 120.572 120.576 120.492 120.497 120.598 120.629 120.506 120.605Y2015W1_min1 %>%
head %>%
zooreg(frequency = 1440)## index BidOpen BidHigh BidLow BidClose AskOpen AskHigh
## 1(1) 2015-01-05 00:01:00 120.474 120.542 120.442 120.502 120.534 120.638
## 1(2) 2015-01-05 00:02:00 120.524 120.570 120.484 120.538 120.592 120.671
## 1(3) 2015-01-05 00:03:00 120.568 120.588 120.533 120.568 120.624 120.678
## 1(4) 2015-01-05 00:04:00 120.570 120.606 120.508 120.539 120.614 120.708
## 1(5) 2015-01-05 00:05:00 120.544 120.594 120.472 120.576 120.668 120.714
## 1(6) 2015-01-05 00:06:00 120.572 120.576 120.492 120.497 120.598 120.629
## AskLow AskClose
## 1(1) 120.520 120.608
## 1(2) 120.566 120.610
## 1(3) 120.588 120.612
## 1(4) 120.566 120.668
## 1(5) 120.506 120.598
## 1(6) 120.506 120.605#Y2015W1_min1 %>% tk_ts(end = c(1440, 7200), frequency = 1440) %>% index %>% as.POSIXct(tz = 'UTC', origin = '1970-01-01')
## https://stats.stackexchange.com/questions/144158/daily-time-series-analysis
## http://manishbarnwal.com/blog/2017/05/03/time_series_and_forecasting_using_R/
#How to extract below index to datetime
#Y2015W1_min1 %>% msts(seasonal.periods=c(1440, 7200)) %>% .[,1] %>% as.numeric %>% as.POSIXct(tz = 'UTC', origin = '1970-01-01') %>% force_tz(tz = 'Europe/Athens')
Y2015W1_min1 %>%
head %>%
msts(seasonal.periods=c(1440, 7200))## Multi-Seasonal Time Series:
## Start: 1 1
## Seasonal Periods: 1440 7200
## Data:
## index BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow
## [1,] 1420383660 120.474 120.542 120.442 120.502 120.534 120.638 120.520
## [2,] 1420383720 120.524 120.570 120.484 120.538 120.592 120.671 120.566
## [3,] 1420383780 120.568 120.588 120.533 120.568 120.624 120.678 120.588
## [4,] 1420383840 120.570 120.606 120.508 120.539 120.614 120.708 120.566
## [5,] 1420383900 120.544 120.594 120.472 120.576 120.668 120.714 120.506
## [6,] 1420383960 120.572 120.576 120.492 120.497 120.598 120.629 120.506
## AskClose
## [1,] 120.608
## [2,] 120.610
## [3,] 120.612
## [4,] 120.668
## [5,] 120.598
## [6,] 120.605ts() only can build a year-month seasonal dataset, otherwise need to decimal numeric to figure out what date within a month accordingly. msts() will be more user friendly which is modelling intra-and-inter seasonal dataset. Now I convert all dataset again from UTC to UTC+2 to be a constant weekly seasonal dataset. Due to the trading day is 5 days and 2 rest days, therefore I set a weekly seasonal period instead of daily.
2018 Time Zones - UTC shows that has no change in No changes, UTC all of the period from 2010 to 2019.
From the Wikipedia UTC page: UTC does not change with a change of seasons, but local time or civil time may change if a time zone jurisdiction observes daylight saving time or summer time. For example, UTC is 5 hours ahead of local time on the east coast of the United States during winter, but 4 hours ahead during summer. In other words, when a time zone observes DST, its offset from UTC changes when there’s a DST transition, but that’s that time zone observing DST, not UTC. Without knowing much about PHP time zone handling, it seems strange to me that you can specify “with DST” or “without DST” in a conversion - the time zones themselves specify when DST kicks in… it shouldn’t have to be something you specify yourself.
Source : Does UTC observe daylight saving time?
Due to the Handling Data for Daylight-Saving and Non-Daylight-Saving for HFT provides the solution for the timezone issue.UTC timezone has no daylight saving issue, therefore the initial trading time will be a problem where I need to cope with.
## -------- eval=FALSE --------------
## Now I simply tidy all datasets and save it prior to start the statistical modelling.
llply(fls[[7]], function(x) {
mbase <- read_rds(x) %>% as_tibble
## Convert the univariate price to be OHLC price in `minutes` unit.
mbase %<>% convertOHLC(.unit = t.unit[2], combine = TRUE) %>%
bind_rows #combined `ask/bid` price
y <- x %>% str_replace_all('.rds$', '_tick-to-min1.rds')
saveRDS(mbase, y)
cat(y, 'saved!\n')
})3.2 1 Minute Data
3.2.1 Get and Tidy Data
Due to fxcm/MarketData updated and provides 1 minute, 1 hour, 1 day datasets recently, here I directly download 1 minute dataset and tidy it.
time is based on EST, because our server is in New Jersey USA. it is 5:00PM at the end of the day, which is shown in GMT as 21:00 day light saving or 22:00 without day light saving.
Source : Inconsistency of trading date time #1
From above quote, we can know even the EST converted to UTC will not be 00:00:00, therefore I refer to Handling data on the days when we switch to daylight savings time and back in R as my solution as UTC+2 (daylight saving UTC+3) will get the desired result.
cr_code <- c('EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 'JPY=X')
names(cr_code) <- c('EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD', 'USDJPY')
fls1 <- llply(names(cr_code), function(x) {
fls <- list.files(paste0(dtr1, x), pattern = '^Y[0-9]{4}W[0-9]{1,2}_m1.rds$')
if (length(fls) > 0) paste0(dtr1, x, '/', fls)
})
names(fls1) <- names(cr_code)
dtr1s <- paste0(dtr1, names(fls1[length(fls1)]))
fs1 <- list.files(dtr1s, pattern = '^Y[0-9]{4}W[0-9]{1,2}_m1.rds$') %>%
str_replace_all('.rds', '')
## Read raw dataset.
# eval(parse(text = paste0(fs, "<- read_rds('", fls[[7]], "')")))## Read raw dataset.
eval(parse(text = paste0(fs1[1], "<- read_rds('", fls1[[5]][1], "') %>% as_tibble")))
## raw dataset
Y2015W1_m1## # A tibble: 7,200 x 9
## DateTime BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow AskClose
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 01/04/2015 2~ 120. 121. 120. 121. 121. 121. 121. 121.
## 2 01/04/2015 2~ 121. 121. 120. 121. 121. 121. 121. 121.
## 3 01/04/2015 2~ 121. 121. 121. 121. 121. 121. 121. 121.
## 4 01/04/2015 2~ 121. 121. 121. 121. 121. 121. 121. 121.
## 5 01/04/2015 2~ 121. 121. 120. 121. 121. 121. 121. 121.
## 6 01/04/2015 2~ 121. 121. 120. 120. 121. 121. 121. 121.
## 7 01/04/2015 2~ 120. 121. 120. 121. 121. 121. 120. 121.
## 8 01/04/2015 2~ 121. 121. 121. 121. 121. 121. 121. 121.
## 9 01/04/2015 2~ 121. 121. 121. 121. 121. 121. 121. 121.
## 10 01/04/2015 2~ 121. 121. 121. 121. 121. 121. 121. 121.
## # ... with 7,190 more rowsNow I try to validate the daylight saving date.
# tsz2 <- llply(fls1[[5]], function(x) {
# y <- read_rds(x) %>% dplyr::filter(DateTime == head(DateTime, 1)|
# DateTime == tail(DateTime, 1)) %>%
# mutate(DateTime = DateTime %>% mdy_hms %>%
# .POSIXct(tz = 'Europe/Athens'),
# diff = difftime(DateTime, lag(DateTime, 1), units = 'mins'))
#
# nch <- y$DateTime[1] %>% substr(nchar(.)+2, nchar(.)+3)
# y %<>% mutate(
# nch = nch, DateTime = if_else(
# nch == '23', DateTime + hours(1), DateTime)) %>%
# dplyr::select(-nch)
# }) %>% bind_rows %>% as_tibble %>% arrange(DateTime)
# saveRDS(tsz2, 'C:/Users/scibr/Documents/GitHub/scibrokes/real-time-fxcm/data/USDJPY/tsz2.rds')
## The daylight saving convertion in not tally.
tsz2 <- read_rds(paste0(dtr1s, '/tsz2.rds')) %>%
dplyr::rename(index = DateTime) %>%
dplyr::filter(index >= ymd_hms('2015-01-05 00:01:00', tz = 'Europe/Athens'))
tsz2## # A tibble: 365 x 10
## index BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-09 23:59:00 119. 119. 118. 118. 119. 119. 119.
## 2 2015-01-12 00:00:00 118. 118. 118. 118. 118. 118. 118.
## 3 2015-01-16 23:56:00 117. 118. 117. 118. 117. 118. 117.
## 4 2015-01-19 00:00:00 117. 117. 117. 117. 117. 118. 117.
## 5 2015-01-23 23:58:00 118. 118. 118. 118. 118. 118. 118.
## 6 2015-01-26 00:00:00 118. 118. 117. 118. 118. 118. 118.
## 7 2015-01-30 23:58:00 117. 118. 117. 118. 118. 118. 118.
## 8 2015-02-02 00:00:00 117. 117. 117. 117. 117. 117. 117.
## 9 2015-02-06 23:59:00 119. 119. 119. 119. 119. 119. 119.
## 10 2015-02-09 00:00:00 119. 119. 119 119. 119. 119. 119.
## # ... with 355 more rows, and 2 more variables: AskClose <dbl>, diff <drtn>## count the frequency of weekly observation.
tsz2 %>% dplyr::count(diff) %>%
kable(caption = 'Count data point') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| diff | n |
|---|---|
| 5395 mins | 1 |
| 5521 mins | 1 |
| 5522 mins | 1 |
| 5638 mins | 2 |
| 5759 mins | 1 |
| 7180 mins | 1 |
| 7187 mins | 1 |
| 7190 mins | 1 |
| 7192 mins | 1 |
| 7193 mins | 1 |
| 7194 mins | 7 |
| 7195 mins | 10 |
| 7196 mins | 13 |
| 7197 mins | 10 |
| 7198 mins | 47 |
| 7199 mins | 85 |
| NA mins | 182 |
## missing observation.
tsz2 %>% dplyr::filter(diff <= 6000)## # A tibble: 6 x 10
## index BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-12-24 20:01:00 120. 120. 120. 120. 120. 120. 120.
## 2 2015-12-31 20:02:00 120. 120. 120. 120. 120. 120. 120.
## 3 2016-12-30 23:58:00 117. 117. 117. 117. 117. 117. 117.
## 4 2017-01-06 23:58:00 117. 117. 117. 117. 117. 117. 117.
## 5 2017-12-29 23:57:00 113. 113. 113. 113. 113. 113. 113.
## 6 2018-01-05 23:59:00 113. 113. 113. 113. 113. 113. 113.
## # ... with 2 more variables: AskClose <dbl>, diff <drtn>From above tables, we can know the daylight saving detection and datetime auto convertion is not tally. Here I united all intial observation started from 00:01:00.
3.3 Completion of Data
3.3.1 Data Selection
binary.com 面试试题 I - 单变量数据缺失值管理 and binary.com面试试题 I - 单变量数据缺失值管理 II compares the missing values dataset and refill the missing value with imputeTS::na.seadec():
- interpolation
- kalman
- locf
- ma
- mean
- random
The papers concludes that the imputeTS::na.seadec(algorithm = 'interpolation') or imputeTS::na.seadec(algorithm = 'kalman') repaired dataset no matter how much of portion of missing value is workable since the MSE and bias is very low. The Amelia::amelia is accurate and the bias and imprecision is small compare to imputeTS::sea.dec when the portion of missing value is small. The papers compare tick-data-to-1min-data and also 1min-data where both datasets gather from FXCM. It is very weird that the tidyr::fill and na.locf both are not too accurate. However, in this paper I use tidy::fill() method to fill the missing value, it will similar with kalman filter method since it will filled up the missing value ascending to fill up with direction down until the bottom of the dataset and then fill up with direction up by descending to fill up initial missing value or top. It will not occured standard error bias like open or close price higher than highest price or lower than lowest price. Moreover, the filled price will not bias a lot from the trend as time goes by.
## tick-data to minute 1 dataset
#tsz <- read_rds('C:/Users/scibr/Documents/GitHub/scibrokes/real-time-fxcm/data/USDJPY/tsz.rds')
tsz %>% dplyr::count(diff) %>%
kable(caption = 'Count data point') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| diff | n |
|---|---|
| 1228 mins | 1 |
| 1276 mins | 1 |
| 1657 mins | 1 |
| 2407 mins | 1 |
| 2449 mins | 1 |
| 2650 mins | 1 |
| 2834 mins | 1 |
| 3777 mins | 1 |
| 5251 mins | 1 |
| 5395 mins | 1 |
| 5495 mins | 1 |
| 5521 mins | 1 |
| 5522 mins | 1 |
| 5620 mins | 1 |
| 5638 mins | 2 |
| 5763 mins | 2 |
| 6355 mins | 1 |
| 6831 mins | 1 |
| 6896 mins | 1 |
| 7180 mins | 1 |
| 7181 mins | 1 |
| 7187 mins | 1 |
| 7190 mins | 1 |
| 7192 mins | 1 |
| 7193 mins | 1 |
| 7194 mins | 7 |
| 7195 mins | 8 |
| 7196 mins | 9 |
| 7197 mins | 8 |
| 7198 mins | 41 |
| 7199 mins | 84 |
| NA mins | 184 |
## minute 1 dataset
#tsz2 <- read_rds('C:/Users/scibr/Documents/GitHub/scibrokes/real-time-fxcm/data/USDJPY/tsz2.rds')
tsz2 %>% dplyr::count(diff) %>%
kable(caption = 'Count data point') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| diff | n |
|---|---|
| 5395 mins | 1 |
| 5521 mins | 1 |
| 5522 mins | 1 |
| 5638 mins | 2 |
| 5759 mins | 1 |
| 7180 mins | 1 |
| 7187 mins | 1 |
| 7190 mins | 1 |
| 7192 mins | 1 |
| 7193 mins | 1 |
| 7194 mins | 7 |
| 7195 mins | 10 |
| 7196 mins | 13 |
| 7197 mins | 10 |
| 7198 mins | 47 |
| 7199 mins | 85 |
| NA mins | 182 |
Above tables show both datasets are incompleted. However, when I tried to check the Y2017W20 and Y2017W20_m1, the tick-dataset only start from 2017-05-15 until 2017-05-17 but the m1-dataset from 2017-05-15 until 2017-05-19. Kindly refer to below comparison.
mean(tsz$diff, na.rm=TRUE)## Time difference of 6886.853 minsmean(tsz2$diff, na.rm=TRUE)## Time difference of 7144.601 minsFrom above comparison, we know the dataset of 1min is better compelete than tick-to-1min dataset.
#left_join(tsz[c(1, ncol(tsz))], tsz2[c(1, ncol(tsz2))])
right_join(tsz[c(1, ncol(tsz))], tsz2[c(1, ncol(tsz2))])## # A tibble: 365 x 2
## index diff
## <dttm> <drtn>
## 1 2015-01-09 23:59:00 7199 mins
## 2 2015-01-12 00:00:00 NA mins
## 3 2015-01-16 23:56:00 7196 mins
## 4 2015-01-19 00:00:00 NA mins
## 5 2015-01-23 23:58:00 7198 mins
## 6 2015-01-26 00:00:00 NA mins
## 7 2015-01-30 23:58:00 7198 mins
## 8 2015-02-02 00:00:00 NA mins
## 9 2015-02-06 23:59:00 7199 mins
## 10 2015-02-09 00:00:00 NA mins
## # ... with 355 more rows- How to fill in missing data in time series? talk about the missing data.
- 4.1 Seasonal ARIMA models
- How to fill in missing data in time series?
- How to Handle Missing Data
Here I compare the mean and get to know the downloaded min1 dataset from FXCM is better than downloaded tick-dataset (converted to min1) from FXCM.
# -------- eval=FALSE -----------
## tick-data to min-1 dataset
data_tm1 <- llply(fls[[7]], function(x) {
y <- read_rds(x) %>%
convertOHLC(combine = TRUE)
yw <- x %>%
str_extract_all('Y[0-9]{4}W[0-9]{1,2}') %>%
str_split_fixed('[A-Z]{1}', 3) %>%
.[,-1]
y %<>% mutate(
year = as.numeric(yw[1]), week = as.numeric(yw[2]), .)
}) %>%
bind_rows %>%
as_tibble %>%
arrange(index)
## min-1 dataset
data_m1 <- llply(fls1[[5]], function(x) {
y <- read_rds(x) %>%
dplyr::rename(index = DateTime) %>%
mutate(index = index %>% mdy_hms %>%
.POSIXct(tz = 'Europe/Athens') %>%
force_tz())
yw <- x %>% str_extract_all('Y[0-9]{4}W[0-9]{1,2}') %>%
str_split_fixed('[A-Z]{1}', 3) %>% .[,-1]
nch <- y$index[1] %>% substr(nchar(.)+2, nchar(.)+3)
y %<>% mutate(
year = as.numeric(yw[1]), week = as.numeric(yw[2]),
nch = nch, index = if_else(
nch == '23', index + hours(1), index)) %>%
dplyr::select(-nch)
}) %>%
bind_rows %>%
as_tibble %>%
arrange(index)# -------- eval=FALSE -----------
#dtm <- seq(ymd_hms('2015-01-01 00:00:00'), ymd_hms('2017-08-31 00:00:00'), by = 'minutes')
#dtm <- seq(from = ymd('2015-01-05'), to = ymd('2018-07-07'), by = 'weeks')
dtm <- data_tm1 %>%
dplyr::select(index, year ,week) %>%
mutate(index = date(index)) %>%
ddply(.(year, week), head, 1) %>%
.[-nrow(.),]
## create a seq of datetime to complete the data point.
dttm <- llply(1:nrow(dtm), function(i) {
x1 <- dtm$index[i] %>%
as.POSIXct %>%
with_tz(tz = 'UTC') %>%
force_tz()
#x2 <- x1 + days(4) + hours(23) + minutes(59)
x2 <- x1 + days(5)
data_frame(index = seq.POSIXt(from = x1 + minutes(1), to = x2, by = '1 min'),
year = dtm[i,2], week = dtm[i,3])
}) %>%
bind_rows %>%
as_tibbleAbove chunk created a sequence of datetime.
## merge dataset
data_m1 <- left_join(dttm, data_m1) %>%
as_tibble %>%
unique %>%
arrange(index)
data_tm1 <- left_join(dttm, data_tm1) %>%
as_tibble %>%
unique %>%
arrange(index)
## https://stackoverflow.com/questions/43212308/na-locf-using-group-by-from-dplyr
## https://stackoverflow.com/questions/233401., eval.expr = TRUE) :
Scanner error: mapping values50/replace-missing-values-na-with-most-recent-non-na-by-group
## https://stackoverflow.com/questions/40040834/replace-na-with-previous-or-next-value-by-group-using-dplyr/40041172
## https://stackoverflow.com/questions/47242643/na-at-the-end-of-column-using-na-locf-function
## https://stackoverflow.com/questions/49578085/na-locf-function-is-changing-data-frame-values-from-int-to-char-in-r
## https://stackoverflow.com/questions/13616965/how-to-fill-nas-with-locf-by-factors-in-data-frame-split-by-country
## https://stackoverflow.com/questions/23340150/replace-missing-values-na-with-most-recent-non-na-by-group
# data_m1 %>%
# group_by(index, week) %>%
# mutate_all(funs(na.locf(., na.rm = FALSE)))
# data_m1 %>% split(data_m1$index) %>%
# llply(function(x) {
# na.locf(na.locf(x), fromLast = TRUE)
# }) %>% do.call(rbind, .)
# data_m1 %<>% ddply(.(index, week), na_locf) %>% as_tibble
#> data_m1 %>% anyNA
#[1] FALSE
data_m1 %<>%
ddply(.(year, week), function(x) {
x %>% fill(year, week, BidOpen, BidHigh, BidLow, BidClose,
AskOpen, AskHigh, AskLow, AskClose) %>% #default direction down
fill(year, week, BidOpen, BidHigh, BidLow, BidClose,
AskOpen, AskHigh, AskLow, AskClose, .direction = 'up')
}) %>%
as_tibble
data_tm1 %<>%
ddply(.(year, week), function(x) {
x %>% fill(year, week, BidOpen, BidHigh, BidLow, BidClose,
AskOpen, AskHigh, AskLow, AskClose) %>% #default direction down
fill(year, week, BidOpen, BidHigh, BidLow, BidClose,
AskOpen, AskHigh, AskLow, AskClose, .direction = 'up')
}) %>%
as_tibble
#> data_m1 %>% anyNA
#[1] TRUE
#> data_m1 %>% filter_all(any_vars(is.na(.)))
## A tibble: 7,200 x 11
# index year week BidOpen BidHigh BidLow BidClose AskOpen AskHigh AskLow AskClose
# <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 2018-01-02 00:01:00 2017 53 NA NA NA NA NA NA NA NA
# 2 2018-01-02 00:02:00 2017 53 NA NA NA NA NA NA NA NA
# 3 2018-01-02 00:03:00 2017 53 NA NA NA NA NA NA NA NA
# 4 2018-01-02 00:04:00 2017 53 NA NA NA NA NA NA NA NA
# 5 2018-01-02 00:05:00 2017 53 NA NA NA NA NA NA NA NA
# 6 2018-01-02 00:06:00 2017 53 NA NA NA NA NA NA NA NA
# 7 2018-01-02 00:07:00 2017 53 NA NA NA NA NA NA NA NA
# 8 2018-01-02 00:08:00 2017 53 NA NA NA NA NA NA NA NA
# 9 2018-01-02 00:09:00 2017 53 NA NA NA NA NA NA NA NA
#10 2018-01-02 00:10:00 2017 53 NA NA NA NA NA NA NA NA
## ... with 7,190 more rows
#> data_tm1 %>% anyNA
#[1] FALSE
#> data_tm1 %>% filter_all(any_vars(is.na(.)))
## A tibble: 0 x 11
## ... with 11 variables: index <dttm>, year <dbl>, week <dbl>, AskOpen <dbl>, AskHigh <dbl>, AskLow <dbl>,
## AskClose <dbl>, BidOpen <dbl>, BidHigh <dbl>, BidLow <dbl>, BidClose <dbl>
saveRDS(data_m1, paste0(dtr1, '/data_m1.rds'))
saveRDS(data_tm1, paste0(dtr1, '/data_tm1.rds'))I don’t use the data.table and feather because of the storage concerns. Kindly refer to [问答] 对大数据如何用R高效处理和[问答] 对大数据如何用R高效处理.
Finally, I filled-up the NA section of data_m1 and data_tm1 and eventually filled up by tidyr::fill function.
3.3.2 Read Data
Due to the files preload all before simulate the statistical modelling will occupy the space. Here I directly read the files and simulate the algorithmic prediction in following sections.
rm(list = ls()[grep('i|j|tz|nch|yw|dtm|dttm|form|data|Y2015W|tsz|tsz2|dc', ls())])
cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X', 'CNY=X', 'JPY=X')
names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')
data_m1 <- read_rds(paste0(dtr1s, '/data_m1.rds'))
tb1 <- data_m1 %>% ddply(.(year, week), head, 1) %>%
kbl('html', caption = 'Weekly Initial Data Point', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
tb1| index | year | week | BidOpen | BidHigh | BidLow | BidClose | AskOpen | AskHigh | AskLow | AskClose |
|---|---|---|---|---|---|---|---|---|---|---|
| 2015-01-05 00:01:00 | 2015 | 1 | 120.502 | 120.570 | 120.484 | 120.538 | 120.608 | 120.671 | 120.566 | 120.610 |
| 2015-01-12 00:01:00 | 2015 | 2 | 118.222 | 118.280 | 118.214 | 118.262 | 118.276 | 118.312 | 118.258 | 118.282 |
| 2015-01-19 00:01:00 | 2015 | 3 | 117.442 | 117.442 | 117.402 | 117.432 | 117.478 | 117.550 | 117.478 | 117.512 |
| 2015-01-26 00:01:00 | 2015 | 4 | 117.500 | 117.504 | 117.467 | 117.482 | 117.508 | 117.524 | 117.502 | 117.507 |
| 2015-02-02 00:01:00 | 2015 | 5 | 116.979 | 117.048 | 116.971 | 117.046 | 117.011 | 117.067 | 116.983 | 117.065 |
| 2015-02-09 00:01:00 | 2015 | 6 | 119.028 | 119.046 | 119.000 | 119.046 | 119.081 | 119.150 | 119.042 | 119.052 |
| 2015-02-16 00:01:00 | 2015 | 7 | 118.562 | 118.628 | 118.544 | 118.628 | 118.587 | 118.649 | 118.548 | 118.646 |
| 2015-02-23 00:01:00 | 2015 | 8 | 119.094 | 119.094 | 119.061 | 119.061 | 119.149 | 119.149 | 119.109 | 119.109 |
| 2015-03-02 00:01:00 | 2015 | 9 | 119.688 | 119.716 | 119.673 | 119.716 | 119.760 | 119.764 | 119.714 | 119.748 |
| 2015-03-09 00:01:00 | 2015 | 10 | 120.800 | 120.836 | 120.800 | 120.836 | 120.920 | 120.920 | 120.889 | 120.889 |
| 2015-03-16 00:01:00 | 2015 | 11 | 121.374 | 121.382 | 121.346 | 121.346 | 121.430 | 121.436 | 121.410 | 121.410 |
| 2015-03-23 00:01:00 | 2015 | 12 | 119.884 | 119.894 | 119.868 | 119.890 | 119.900 | 119.902 | 119.897 | 119.898 |
| 2015-03-30 00:01:00 | 2015 | 13 | 119.216 | 119.220 | 119.203 | 119.203 | 119.247 | 119.253 | 119.230 | 119.230 |
| 2015-04-06 00:01:00 | 2015 | 14 | 118.845 | 118.845 | 118.839 | 118.839 | 118.915 | 118.951 | 118.915 | 118.943 |
| 2015-04-13 00:01:00 | 2015 | 15 | 120.299 | 120.311 | 120.299 | 120.311 | 120.385 | 120.386 | 120.368 | 120.368 |
| 2015-04-20 00:01:00 | 2015 | 16 | 118.985 | 118.993 | 118.985 | 118.993 | 119.014 | 119.047 | 119.014 | 119.047 |
| 2015-04-27 00:01:00 | 2015 | 17 | 118.864 | 118.877 | 118.864 | 118.876 | 118.906 | 118.906 | 118.903 | 118.903 |
| 2015-05-04 00:01:00 | 2015 | 18 | 120.227 | 120.227 | 120.226 | 120.226 | 120.242 | 120.242 | 120.242 | 120.242 |
| 2015-05-11 00:01:00 | 2015 | 19 | 119.652 | 119.688 | 119.644 | 119.658 | 119.684 | 119.731 | 119.676 | 119.719 |
| 2015-05-18 00:01:00 | 2015 | 20 | 119.214 | 119.255 | 119.214 | 119.255 | 119.308 | 119.314 | 119.308 | 119.312 |
| 2015-05-25 00:01:00 | 2015 | 21 | 121.494 | 121.494 | 121.488 | 121.488 | 121.516 | 121.516 | 121.512 | 121.512 |
| 2015-06-01 00:01:00 | 2015 | 22 | 124.076 | 124.084 | 124.072 | 124.072 | 124.100 | 124.106 | 124.094 | 124.096 |
| 2015-06-08 00:01:00 | 2015 | 23 | 125.578 | 125.588 | 125.566 | 125.568 | 125.598 | 125.610 | 125.590 | 125.590 |
| 2015-06-15 00:01:00 | 2015 | 24 | 123.174 | 123.174 | 123.130 | 123.159 | 123.276 | 123.276 | 123.186 | 123.189 |
| 2015-06-22 00:01:00 | 2015 | 25 | 122.955 | 122.957 | 122.922 | 122.922 | 122.968 | 122.968 | 122.936 | 122.936 |
| 2015-06-29 00:01:00 | 2015 | 26 | 122.728 | 122.736 | 122.667 | 122.707 | 122.740 | 122.806 | 122.692 | 122.740 |
| 2015-07-06 00:01:00 | 2015 | 27 | 121.968 | 122.004 | 121.951 | 121.986 | 121.992 | 122.128 | 121.978 | 122.002 |
| 2015-07-13 00:01:00 | 2015 | 28 | 122.218 | 122.224 | 122.178 | 122.204 | 122.332 | 122.332 | 122.206 | 122.286 |
| 2015-07-20 00:01:00 | 2015 | 29 | 124.044 | 124.044 | 124.036 | 124.036 | 124.058 | 124.058 | 124.048 | 124.048 |
| 2015-07-27 00:01:00 | 2015 | 30 | 123.728 | 123.760 | 123.726 | 123.760 | 123.800 | 123.830 | 123.770 | 123.830 |
| 2015-08-03 00:01:00 | 2015 | 31 | 123.850 | 123.860 | 123.850 | 123.860 | 123.904 | 123.906 | 123.904 | 123.906 |
| 2015-08-10 00:01:00 | 2015 | 32 | 124.140 | 124.140 | 124.127 | 124.127 | 124.204 | 124.204 | 124.204 | 124.204 |
| 2015-08-17 00:01:00 | 2015 | 33 | 124.228 | 124.268 | 124.228 | 124.255 | 124.356 | 124.372 | 124.352 | 124.363 |
| 2015-08-24 00:01:00 | 2015 | 34 | 121.882 | 121.894 | 121.882 | 121.890 | 121.902 | 121.920 | 121.902 | 121.918 |
| 2015-08-31 00:01:00 | 2015 | 35 | 121.576 | 121.622 | 121.576 | 121.616 | 121.682 | 121.686 | 121.624 | 121.632 |
| 2015-09-07 00:01:00 | 2015 | 36 | 118.864 | 118.906 | 118.864 | 118.874 | 118.918 | 118.926 | 118.914 | 118.918 |
| 2015-09-14 00:01:00 | 2015 | 37 | 120.488 | 120.489 | 120.472 | 120.472 | 120.602 | 120.603 | 120.596 | 120.596 |
| 2015-09-21 00:01:00 | 2015 | 38 | 120.104 | 120.112 | 120.102 | 120.102 | 120.136 | 120.144 | 120.134 | 120.136 |
| 2015-09-28 00:01:00 | 2015 | 39 | 120.510 | 120.510 | 120.502 | 120.502 | 120.536 | 120.543 | 120.536 | 120.543 |
| 2015-10-05 00:01:00 | 2015 | 40 | 119.982 | 119.987 | 119.968 | 119.986 | 120.008 | 120.072 | 120.008 | 120.070 |
| 2015-10-12 00:01:00 | 2015 | 41 | 120.166 | 120.166 | 120.162 | 120.164 | 120.199 | 120.202 | 120.194 | 120.199 |
| 2015-10-19 00:01:00 | 2015 | 42 | 119.351 | 119.351 | 119.346 | 119.346 | 119.429 | 119.434 | 119.429 | 119.434 |
| 2015-10-26 00:01:00 | 2015 | 43 | 121.450 | 121.468 | 121.448 | 121.454 | 121.518 | 121.520 | 121.470 | 121.470 |
| 2015-11-02 00:01:00 | 2015 | 44 | 120.450 | 120.462 | 120.392 | 120.396 | 120.479 | 120.483 | 120.402 | 120.430 |
| 2015-11-09 00:01:00 | 2015 | 45 | 123.254 | 123.302 | 123.254 | 123.302 | 123.362 | 123.362 | 123.319 | 123.319 |
| 2015-11-16 00:01:00 | 2015 | 46 | 122.286 | 122.310 | 122.280 | 122.293 | 122.299 | 122.350 | 122.295 | 122.301 |
| 2015-11-23 00:01:00 | 2015 | 47 | 122.801 | 122.821 | 122.801 | 122.816 | 122.920 | 122.925 | 122.919 | 122.924 |
| 2015-11-30 00:01:00 | 2015 | 48 | 122.810 | 122.811 | 122.810 | 122.811 | 122.829 | 122.830 | 122.829 | 122.830 |
| 2015-12-07 00:01:00 | 2015 | 49 | 123.191 | 123.191 | 123.190 | 123.190 | 123.240 | 123.240 | 123.239 | 123.239 |
| 2015-12-14 00:01:00 | 2015 | 50 | 121.138 | 121.147 | 120.965 | 121.100 | 121.158 | 121.158 | 121.045 | 121.110 |
| 2015-12-21 00:01:00 | 2015 | 51 | 121.226 | 121.226 | 121.226 | 121.226 | 121.258 | 121.260 | 121.258 | 121.260 |
| 2015-12-28 00:01:00 | 2015 | 52 | 120.230 | 120.270 | 120.216 | 120.223 | 120.328 | 120.330 | 120.260 | 120.328 |
| 2016-01-04 00:01:00 | 2016 | 1 | 120.199 | 120.205 | 120.199 | 120.205 | 120.241 | 120.241 | 120.234 | 120.235 |
| 2016-01-11 00:01:00 | 2016 | 2 | 117.139 | 117.164 | 117.131 | 117.164 | 117.158 | 117.228 | 117.145 | 117.200 |
| 2016-01-18 00:01:00 | 2016 | 3 | 116.699 | 116.834 | 116.682 | 116.828 | 116.752 | 116.882 | 116.750 | 116.872 |
| 2016-01-25 00:01:00 | 2016 | 4 | 118.620 | 118.689 | 118.620 | 118.689 | 118.701 | 118.780 | 118.700 | 118.707 |
| 2016-02-01 00:01:00 | 2016 | 5 | 121.298 | 121.298 | 121.198 | 121.258 | 121.325 | 121.325 | 121.244 | 121.277 |
| 2016-02-08 00:01:00 | 2016 | 6 | 116.779 | 116.799 | 116.779 | 116.799 | 116.877 | 116.899 | 116.877 | 116.899 |
| 2016-02-15 00:01:00 | 2016 | 7 | 113.382 | 113.382 | 113.376 | 113.382 | 113.418 | 113.419 | 113.418 | 113.418 |
| 2016-02-22 00:01:00 | 2016 | 8 | 112.558 | 112.560 | 112.536 | 112.536 | 112.618 | 112.624 | 112.616 | 112.624 |
| 2016-02-29 00:01:00 | 2016 | 9 | 113.942 | 113.948 | 113.940 | 113.946 | 113.994 | 113.999 | 113.992 | 113.998 |
| 2016-03-07 00:01:00 | 2016 | 10 | 113.918 | 113.918 | 113.913 | 113.913 | 113.982 | 113.982 | 113.982 | 113.982 |
| 2016-03-14 00:01:00 | 2016 | 11 | 113.935 | 113.936 | 113.924 | 113.924 | 113.962 | 113.968 | 113.956 | 113.958 |
| 2016-03-21 00:01:00 | 2016 | 12 | 111.518 | 111.518 | 111.512 | 111.512 | 111.612 | 111.612 | 111.602 | 111.602 |
| 2016-03-28 00:01:00 | 2016 | 13 | 113.156 | 113.156 | 113.149 | 113.149 | 113.234 | 113.240 | 113.234 | 113.240 |
| 2016-04-04 00:01:00 | 2016 | 14 | 111.590 | 111.594 | 111.590 | 111.590 | 111.658 | 111.662 | 111.658 | 111.660 |
| 2016-04-11 00:01:00 | 2016 | 15 | 107.932 | 107.992 | 107.932 | 107.992 | 108.006 | 108.066 | 108.006 | 108.020 |
| 2016-04-18 00:01:00 | 2016 | 16 | 108.173 | 108.220 | 108.173 | 108.188 | 108.252 | 108.284 | 108.252 | 108.274 |
| 2016-04-25 00:01:00 | 2016 | 17 | 111.846 | 111.848 | 111.844 | 111.848 | 111.882 | 111.892 | 111.882 | 111.892 |
| 2016-05-02 00:01:00 | 2016 | 18 | 106.230 | 106.254 | 106.216 | 106.244 | 106.274 | 106.310 | 106.273 | 106.280 |
| 2016-05-09 00:01:00 | 2016 | 19 | 107.068 | 107.068 | 107.066 | 107.067 | 107.106 | 107.108 | 107.106 | 107.108 |
| 2016-05-16 00:01:00 | 2016 | 20 | 108.592 | 108.595 | 108.589 | 108.595 | 108.654 | 108.674 | 108.654 | 108.670 |
| 2016-05-23 00:01:00 | 2016 | 21 | 110.138 | 110.138 | 110.134 | 110.136 | 110.176 | 110.176 | 110.172 | 110.172 |
| 2016-05-30 00:01:00 | 2016 | 22 | 110.414 | 110.428 | 110.410 | 110.428 | 110.432 | 110.456 | 110.432 | 110.451 |
| 2016-06-06 00:01:00 | 2016 | 23 | 106.549 | 106.555 | 106.547 | 106.555 | 106.575 | 106.575 | 106.573 | 106.575 |
| 2016-06-13 00:01:00 | 2016 | 24 | 106.800 | 106.833 | 106.796 | 106.812 | 106.890 | 106.892 | 106.884 | 106.884 |
| 2016-06-20 00:01:00 | 2016 | 25 | 104.681 | 104.692 | 104.657 | 104.671 | 104.739 | 104.744 | 104.723 | 104.743 |
| 2016-06-27 00:01:00 | 2016 | 26 | 101.519 | 101.521 | 101.510 | 101.519 | 101.539 | 101.550 | 101.527 | 101.546 |
| 2016-07-04 00:01:00 | 2016 | 27 | 102.594 | 102.598 | 102.594 | 102.598 | 102.636 | 102.647 | 102.634 | 102.647 |
| 2016-07-11 00:01:00 | 2016 | 28 | 100.589 | 100.590 | 100.589 | 100.590 | 100.653 | 100.653 | 100.653 | 100.653 |
| 2016-07-18 00:01:00 | 2016 | 29 | 105.333 | 105.342 | 105.331 | 105.342 | 105.369 | 105.369 | 105.368 | 105.368 |
| 2016-07-25 00:01:00 | 2016 | 30 | 106.116 | 106.129 | 106.089 | 106.089 | 106.180 | 106.186 | 106.175 | 106.176 |
| 2016-08-01 00:01:00 | 2016 | 31 | 102.284 | 102.284 | 102.205 | 102.234 | 102.376 | 102.376 | 102.274 | 102.284 |
| 2016-08-08 00:01:00 | 2016 | 32 | 101.937 | 101.946 | 101.937 | 101.944 | 101.996 | 102.012 | 101.964 | 102.012 |
| 2016-08-15 00:01:00 | 2016 | 33 | 101.115 | 101.124 | 101.115 | 101.124 | 101.157 | 101.206 | 101.157 | 101.206 |
| 2016-08-22 00:01:00 | 2016 | 34 | 100.748 | 100.748 | 100.746 | 100.748 | 100.811 | 100.811 | 100.784 | 100.784 |
| 2016-08-29 00:01:00 | 2016 | 35 | 102.039 | 102.096 | 102.026 | 102.076 | 102.116 | 102.122 | 102.052 | 102.102 |
| 2016-09-05 00:01:00 | 2016 | 36 | 104.078 | 104.084 | 104.078 | 104.078 | 104.146 | 104.146 | 104.146 | 104.146 |
| 2016-09-12 00:01:00 | 2016 | 37 | 102.552 | 102.588 | 102.552 | 102.571 | 102.650 | 102.651 | 102.650 | 102.651 |
| 2016-09-19 00:01:00 | 2016 | 38 | 102.148 | 102.178 | 102.148 | 102.178 | 102.246 | 102.266 | 102.204 | 102.220 |
| 2016-09-26 00:01:00 | 2016 | 39 | 101.029 | 101.059 | 101.029 | 101.038 | 101.079 | 101.135 | 101.079 | 101.132 |
| 2016-10-03 00:01:00 | 2016 | 40 | 101.196 | 101.198 | 101.194 | 101.198 | 101.276 | 101.284 | 101.276 | 101.284 |
| 2016-10-10 00:01:00 | 2016 | 41 | 103.292 | 103.296 | 103.242 | 103.252 | 103.374 | 103.374 | 103.299 | 103.299 |
| 2016-10-17 00:01:00 | 2016 | 42 | 104.327 | 104.327 | 104.317 | 104.326 | 104.340 | 104.344 | 104.340 | 104.340 |
| 2016-10-24 00:01:00 | 2016 | 43 | 103.816 | 103.820 | 103.816 | 103.820 | 103.873 | 103.873 | 103.873 | 103.873 |
| 2016-10-31 00:01:00 | 2016 | 44 | 104.404 | 104.412 | 104.401 | 104.411 | 104.502 | 104.502 | 104.489 | 104.493 |
| 2016-11-07 00:01:00 | 2016 | 45 | 104.033 | 104.033 | 103.769 | 103.769 | 104.117 | 104.117 | 103.829 | 103.829 |
| 2016-11-14 00:01:00 | 2016 | 46 | 106.848 | 106.848 | 106.767 | 106.812 | 106.880 | 106.880 | 106.792 | 106.822 |
| 2016-11-21 00:01:00 | 2016 | 47 | 110.898 | 110.980 | 110.898 | 110.958 | 110.982 | 110.995 | 110.980 | 110.986 |
| 2016-11-28 00:01:00 | 2016 | 48 | 112.798 | 112.872 | 112.798 | 112.872 | 112.872 | 112.902 | 112.872 | 112.902 |
| 2016-12-05 00:01:00 | 2016 | 49 | 113.223 | 113.248 | 113.176 | 113.182 | 113.372 | 113.372 | 113.186 | 113.196 |
| 2016-12-12 00:01:00 | 2016 | 50 | 115.403 | 115.412 | 115.403 | 115.408 | 115.452 | 115.452 | 115.437 | 115.452 |
| 2016-12-19 00:01:00 | 2016 | 51 | 117.948 | 117.948 | 117.948 | 117.948 | 117.972 | 117.972 | 117.956 | 117.972 |
| 2016-12-27 00:01:00 | 2016 | 52 | 117.242 | 117.242 | 117.189 | 117.195 | 117.322 | 117.322 | 117.195 | 117.198 |
| 2017-01-03 00:01:00 | 2017 | 1 | 116.978 | 117.523 | 116.978 | 117.454 | 117.076 | 117.528 | 117.076 | 117.453 |
| 2017-01-09 00:01:00 | 2017 | 2 | 117.009 | 117.009 | 117.002 | 117.002 | 117.031 | 117.031 | 117.012 | 117.012 |
| 2017-01-16 00:01:00 | 2017 | 3 | 114.299 | 114.378 | 114.299 | 114.309 | 114.381 | 114.392 | 114.381 | 114.391 |
| 2017-01-23 00:01:00 | 2017 | 4 | 114.354 | 114.364 | 114.338 | 114.348 | 114.400 | 114.430 | 114.392 | 114.420 |
| 2017-01-30 00:01:00 | 2017 | 5 | 114.760 | 114.800 | 114.760 | 114.784 | 114.790 | 114.820 | 114.784 | 114.820 |
| 2017-02-06 00:01:00 | 2017 | 6 | 112.442 | 112.455 | 112.440 | 112.444 | 112.520 | 112.520 | 112.480 | 112.480 |
| 2017-02-13 00:01:00 | 2017 | 7 | 113.545 | 113.545 | 113.530 | 113.530 | 113.625 | 113.625 | 113.625 | 113.625 |
| 2017-02-20 00:01:00 | 2017 | 8 | 112.864 | 112.882 | 112.864 | 112.879 | 112.903 | 112.908 | 112.903 | 112.908 |
| 2017-02-27 00:01:00 | 2017 | 9 | 112.108 | 112.125 | 112.108 | 112.125 | 112.192 | 112.205 | 112.192 | 112.204 |
| 2017-03-06 00:01:00 | 2017 | 10 | 113.855 | 113.894 | 113.855 | 113.894 | 113.903 | 113.916 | 113.903 | 113.913 |
| 2017-03-13 00:01:00 | 2017 | 11 | 114.725 | 114.725 | 114.689 | 114.707 | 114.784 | 114.787 | 114.743 | 114.784 |
| 2017-03-20 00:01:00 | 2017 | 12 | 112.656 | 112.681 | 112.656 | 112.673 | 112.749 | 112.757 | 112.749 | 112.757 |
| 2017-03-27 00:01:00 | 2017 | 13 | 110.861 | 110.893 | 110.815 | 110.893 | 110.917 | 110.975 | 110.898 | 110.935 |
| 2017-04-03 00:01:00 | 2017 | 14 | 111.414 | 111.414 | 111.329 | 111.329 | 111.503 | 111.503 | 111.418 | 111.418 |
| 2017-04-10 00:01:00 | 2017 | 15 | 111.029 | 111.066 | 111.015 | 111.018 | 111.118 | 111.118 | 111.081 | 111.081 |
| 2017-04-17 00:01:00 | 2017 | 16 | 108.691 | 108.741 | 108.691 | 108.741 | 108.790 | 108.830 | 108.790 | 108.830 |
| 2017-04-24 00:01:00 | 2017 | 17 | 110.518 | 110.518 | 110.394 | 110.457 | 110.729 | 110.729 | 110.502 | 110.516 |
| 2017-05-01 00:01:00 | 2017 | 18 | 111.240 | 111.330 | 111.240 | 111.330 | 111.334 | 111.394 | 111.334 | 111.389 |
| 2017-05-08 00:01:00 | 2017 | 19 | 112.931 | 112.949 | 112.922 | 112.946 | 113.004 | 113.022 | 112.980 | 112.984 |
| 2017-05-15 00:01:00 | 2017 | 20 | 113.124 | 113.171 | 113.124 | 113.170 | 113.205 | 113.205 | 113.194 | 113.194 |
| 2017-05-22 00:01:00 | 2017 | 21 | 110.985 | 111.050 | 110.985 | 111.047 | 111.084 | 111.084 | 111.069 | 111.069 |
| 2017-05-29 00:01:00 | 2017 | 22 | 111.178 | 111.210 | 111.178 | 111.210 | 111.277 | 111.309 | 111.277 | 111.309 |
| 2017-06-05 00:01:00 | 2017 | 23 | 110.352 | 110.391 | 110.352 | 110.391 | 110.396 | 110.483 | 110.396 | 110.480 |
| 2017-06-12 00:01:00 | 2017 | 24 | 110.309 | 110.309 | 110.291 | 110.304 | 110.342 | 110.342 | 110.333 | 110.333 |
| 2017-06-19 00:01:00 | 2017 | 25 | 110.881 | 110.881 | 110.878 | 110.878 | 110.945 | 110.945 | 110.922 | 110.924 |
| 2017-06-26 00:01:00 | 2017 | 26 | 111.186 | 111.186 | 111.178 | 111.184 | 111.256 | 111.256 | 111.235 | 111.235 |
| 2017-07-03 00:01:00 | 2017 | 27 | 112.098 | 112.125 | 112.085 | 112.125 | 112.122 | 112.179 | 112.122 | 112.176 |
| 2017-07-10 00:01:00 | 2017 | 28 | 113.863 | 113.899 | 113.863 | 113.899 | 113.897 | 113.918 | 113.897 | 113.918 |
| 2017-07-17 00:01:00 | 2017 | 29 | 112.452 | 112.480 | 112.452 | 112.480 | 112.485 | 112.515 | 112.485 | 112.504 |
| 2017-07-24 00:01:00 | 2017 | 30 | 111.106 | 111.106 | 111.097 | 111.106 | 111.138 | 111.138 | 111.133 | 111.133 |
| 2017-07-31 00:01:00 | 2017 | 31 | 110.653 | 110.653 | 110.636 | 110.636 | 110.677 | 110.677 | 110.668 | 110.668 |
| 2017-08-07 00:01:00 | 2017 | 32 | 110.697 | 110.702 | 110.686 | 110.702 | 110.727 | 110.745 | 110.726 | 110.738 |
| 2017-08-14 00:01:00 | 2017 | 33 | 109.153 | 109.153 | 109.153 | 109.153 | 109.187 | 109.187 | 109.184 | 109.184 |
| 2017-08-21 00:01:00 | 2017 | 34 | 109.313 | 109.346 | 109.313 | 109.346 | 109.347 | 109.377 | 109.347 | 109.377 |
| 2017-08-28 00:01:00 | 2017 | 35 | 109.154 | 109.176 | 109.154 | 109.176 | 109.223 | 109.223 | 109.206 | 109.206 |
| 2017-09-04 00:01:00 | 2017 | 36 | 109.532 | 109.556 | 109.528 | 109.532 | 109.558 | 109.592 | 109.554 | 109.566 |
| 2017-09-11 00:01:00 | 2017 | 37 | 108.196 | 108.196 | 108.188 | 108.190 | 108.212 | 108.246 | 108.206 | 108.230 |
| 2017-09-18 00:01:00 | 2017 | 38 | 111.042 | 111.060 | 111.040 | 111.060 | 111.094 | 111.094 | 111.094 | 111.094 |
| 2017-09-25 00:01:00 | 2017 | 39 | 112.146 | 112.161 | 112.146 | 112.148 | 112.202 | 112.202 | 112.178 | 112.182 |
| 2017-10-02 00:01:00 | 2017 | 40 | 112.538 | 112.538 | 112.538 | 112.538 | 112.606 | 112.608 | 112.606 | 112.608 |
| 2017-10-09 00:01:00 | 2017 | 41 | 112.570 | 112.570 | 112.550 | 112.569 | 112.622 | 112.622 | 112.600 | 112.600 |
| 2017-10-16 00:01:00 | 2017 | 42 | 111.748 | 111.786 | 111.748 | 111.784 | 111.782 | 111.806 | 111.782 | 111.800 |
| 2017-10-23 00:01:00 | 2017 | 43 | 113.868 | 113.872 | 113.844 | 113.846 | 113.896 | 113.896 | 113.878 | 113.878 |
| 2017-10-30 00:01:00 | 2017 | 44 | 113.718 | 113.723 | 113.718 | 113.723 | 113.746 | 113.746 | 113.741 | 113.741 |
| 2017-11-06 00:01:00 | 2017 | 45 | 114.001 | 114.015 | 114.001 | 114.015 | 114.049 | 114.049 | 114.035 | 114.048 |
| 2017-11-13 00:01:00 | 2017 | 46 | 113.492 | 113.538 | 113.492 | 113.494 | 113.572 | 113.574 | 113.544 | 113.546 |
| 2017-11-20 00:01:00 | 2017 | 47 | 112.120 | 112.120 | 112.119 | 112.119 | 112.168 | 112.168 | 112.167 | 112.167 |
| 2017-11-27 00:01:00 | 2017 | 48 | 111.500 | 111.501 | 111.500 | 111.500 | 111.548 | 111.549 | 111.548 | 111.548 |
| 2017-12-04 00:01:00 | 2017 | 49 | 112.776 | 112.778 | 112.707 | 112.726 | 112.792 | 112.800 | 112.750 | 112.774 |
| 2017-12-11 00:01:00 | 2017 | 50 | 113.526 | 113.528 | 113.526 | 113.528 | 113.566 | 113.566 | 113.562 | 113.562 |
| 2017-12-18 00:01:00 | 2017 | 51 | 112.714 | 112.717 | 112.714 | 112.717 | 112.734 | 112.734 | 112.734 | 112.734 |
| 2017-12-26 00:01:00 | 2017 | 52 | 113.265 | 113.287 | 113.265 | 113.287 | 113.343 | 113.343 | 113.287 | 113.289 |
| 2018-01-02 00:01:00 | 2017 | 53 | NA | NA | NA | NA | NA | NA | NA | NA |
| 2018-01-02 00:01:00 | 2018 | 1 | 112.596 | 112.601 | 112.596 | 112.601 | 112.650 | 112.658 | 112.650 | 112.658 |
| 2018-01-08 00:01:00 | 2018 | 2 | 113.116 | 113.121 | 113.116 | 113.121 | 113.152 | 113.152 | 113.150 | 113.152 |
| 2018-01-15 00:01:00 | 2018 | 3 | 111.075 | 111.082 | 111.075 | 111.081 | 111.113 | 111.113 | 111.104 | 111.104 |
| 2018-01-22 00:01:00 | 2018 | 4 | 110.543 | 110.543 | 110.517 | 110.517 | 110.602 | 110.602 | 110.570 | 110.570 |
| 2018-01-29 00:01:00 | 2018 | 5 | 108.685 | 108.700 | 108.684 | 108.693 | 108.733 | 108.746 | 108.732 | 108.732 |
| 2018-02-05 00:01:00 | 2018 | 6 | 110.200 | 110.206 | 110.172 | 110.172 | 110.248 | 110.248 | 110.228 | 110.232 |
| 2018-02-12 00:01:00 | 2018 | 7 | 108.858 | 108.862 | 108.832 | 108.836 | 108.896 | 108.898 | 108.858 | 108.858 |
| 2018-02-19 00:01:00 | 2018 | 8 | 106.328 | 106.328 | 106.298 | 106.304 | 106.382 | 106.382 | 106.348 | 106.348 |
| 2018-02-26 00:01:00 | 2018 | 9 | 107.106 | 107.116 | 107.092 | 107.092 | 107.132 | 107.132 | 107.114 | 107.114 |
| 2018-03-05 00:01:00 | 2018 | 10 | 105.500 | 105.500 | 105.494 | 105.496 | 105.554 | 105.556 | 105.552 | 105.552 |
| 2018-03-12 00:01:00 | 2018 | 11 | 106.635 | 106.642 | 106.635 | 106.642 | 106.673 | 106.680 | 106.673 | 106.680 |
| 2018-03-19 00:01:00 | 2018 | 12 | 105.915 | 105.917 | 105.904 | 105.915 | 105.926 | 105.949 | 105.916 | 105.942 |
| 2018-03-26 00:01:00 | 2018 | 13 | 104.641 | 104.642 | 104.640 | 104.642 | 104.694 | 104.695 | 104.678 | 104.695 |
| 2018-04-02 00:01:00 | 2018 | 14 | 106.260 | 106.260 | 106.237 | 106.237 | 106.312 | 106.312 | 106.273 | 106.274 |
| 2018-04-09 00:01:00 | 2018 | 15 | 106.937 | 106.944 | 106.937 | 106.944 | 106.989 | 106.992 | 106.989 | 106.992 |
| 2018-04-16 00:01:00 | 2018 | 16 | 107.338 | 107.470 | 107.338 | 107.462 | 107.385 | 107.525 | 107.385 | 107.510 |
| 2018-04-23 00:01:00 | 2018 | 17 | 107.766 | 107.770 | 107.762 | 107.770 | 107.816 | 107.816 | 107.816 | 107.816 |
| 2018-04-30 00:01:00 | 2018 | 18 | 109.055 | 109.066 | 109.020 | 109.066 | 109.083 | 109.091 | 109.046 | 109.089 |
| 2018-05-07 00:01:00 | 2018 | 19 | 109.109 | 109.109 | 109.108 | 109.108 | 109.127 | 109.127 | 109.126 | 109.126 |
| 2018-05-14 00:01:00 | 2018 | 20 | 109.384 | 109.384 | 109.335 | 109.346 | 109.443 | 109.443 | 109.389 | 109.394 |
| 2018-05-21 00:01:00 | 2018 | 21 | 110.869 | 110.900 | 110.866 | 110.866 | 110.897 | 110.917 | 110.894 | 110.909 |
| 2018-05-28 00:01:00 | 2018 | 22 | 109.738 | 109.746 | 109.702 | 109.740 | 109.750 | 109.762 | 109.745 | 109.760 |
| 2018-06-04 00:01:00 | 2018 | 23 | 109.454 | 109.454 | 109.450 | 109.450 | 109.480 | 109.480 | 109.456 | 109.456 |
| 2018-06-11 00:01:00 | 2018 | 24 | 109.284 | 109.296 | 109.284 | 109.292 | 109.324 | 109.350 | 109.324 | 109.350 |
| 2018-06-18 00:01:00 | 2018 | 25 | 110.665 | 110.676 | 110.665 | 110.665 | 110.700 | 110.719 | 110.700 | 110.718 |
| 2018-06-25 00:01:00 | 2018 | 26 | 109.841 | 109.847 | 109.841 | 109.847 | 109.889 | 109.895 | 109.884 | 109.895 |
| 2018-07-02 00:01:00 | 2018 | 27 | 110.680 | 110.680 | 110.667 | 110.667 | 110.720 | 110.726 | 110.720 | 110.726 |
tb2 <- data_m1 %>% ddply(.(year, week), tail, 1) %>%
kbl('html', caption = 'Weekly Final Data Point', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
tb2| index | year | week | BidOpen | BidHigh | BidLow | BidClose | AskOpen | AskHigh | AskLow | AskClose |
|---|---|---|---|---|---|---|---|---|---|---|
| 2015-01-10 | 2015 | 1 | 118.522 | 118.522 | 118.495 | 118.495 | 118.556 | 118.601 | 118.556 | 118.601 |
| 2015-01-17 | 2015 | 2 | 117.462 | 117.554 | 117.461 | 117.548 | 117.490 | 117.669 | 117.482 | 117.669 |
| 2015-01-24 | 2015 | 3 | 117.724 | 117.770 | 117.714 | 117.732 | 117.834 | 117.836 | 117.796 | 117.816 |
| 2015-01-31 | 2015 | 4 | 117.493 | 117.534 | 117.438 | 117.528 | 117.548 | 117.614 | 117.548 | 117.576 |
| 2015-02-07 | 2015 | 5 | 119.134 | 119.134 | 119.090 | 119.090 | 119.158 | 119.222 | 119.158 | 119.222 |
| 2015-02-14 | 2015 | 6 | 118.719 | 118.719 | 118.696 | 118.696 | 118.919 | 118.944 | 118.919 | 118.944 |
| 2015-02-21 | 2015 | 7 | 119.050 | 119.056 | 118.966 | 119.010 | 119.098 | 119.116 | 119.036 | 119.042 |
| 2015-02-28 | 2015 | 8 | 119.596 | 119.636 | 119.576 | 119.576 | 119.620 | 119.710 | 119.618 | 119.704 |
| 2015-03-07 | 2015 | 9 | 120.784 | 120.784 | 120.708 | 120.708 | 120.804 | 120.885 | 120.804 | 120.885 |
| 2015-03-14 | 2015 | 10 | 121.426 | 121.428 | 121.350 | 121.416 | 121.448 | 121.496 | 121.388 | 121.458 |
| 2015-03-21 | 2015 | 11 | 120.048 | 120.052 | 120.008 | 120.018 | 120.072 | 120.100 | 120.056 | 120.068 |
| 2015-03-28 | 2015 | 12 | 119.112 | 119.112 | 119.109 | 119.109 | 119.150 | 119.171 | 119.150 | 119.171 |
| 2015-04-04 | 2015 | 13 | 118.929 | 118.929 | 118.928 | 118.928 | 119.016 | 119.041 | 119.016 | 119.041 |
| 2015-04-11 | 2015 | 14 | 120.170 | 120.174 | 120.170 | 120.174 | 120.206 | 120.261 | 120.206 | 120.261 |
| 2015-04-18 | 2015 | 15 | 118.889 | 118.897 | 118.889 | 118.897 | 118.971 | 118.978 | 118.971 | 118.978 |
| 2015-04-25 | 2015 | 16 | 118.906 | 118.930 | 118.906 | 118.926 | 118.974 | 119.020 | 118.974 | 119.015 |
| 2015-05-02 | 2015 | 17 | 120.202 | 120.202 | 120.171 | 120.171 | 120.256 | 120.256 | 120.251 | 120.251 |
| 2015-05-09 | 2015 | 18 | 119.754 | 119.771 | 119.754 | 119.771 | 119.806 | 119.870 | 119.806 | 119.870 |
| 2015-05-16 | 2015 | 19 | 119.366 | 119.366 | 119.352 | 119.359 | 119.418 | 119.467 | 119.418 | 119.450 |
| 2015-05-23 | 2015 | 20 | 121.544 | 121.544 | 121.500 | 121.500 | 121.576 | 121.591 | 121.576 | 121.581 |
| 2015-05-30 | 2015 | 21 | 124.130 | 124.130 | 124.112 | 124.112 | 124.154 | 124.191 | 124.154 | 124.191 |
| 2015-06-06 | 2015 | 22 | 125.577 | 125.588 | 125.575 | 125.576 | 125.638 | 125.667 | 125.638 | 125.655 |
| 2015-06-13 | 2015 | 23 | 123.359 | 123.359 | 123.349 | 123.349 | 123.446 | 123.471 | 123.446 | 123.471 |
| 2015-06-20 | 2015 | 24 | 122.672 | 122.672 | 122.632 | 122.632 | 122.724 | 122.725 | 122.711 | 122.711 |
| 2015-06-27 | 2015 | 25 | 123.884 | 123.884 | 123.809 | 123.809 | 123.912 | 123.926 | 123.901 | 123.901 |
| 2015-07-04 | 2015 | 26 | 122.854 | 122.854 | 122.799 | 122.799 | 122.914 | 122.934 | 122.888 | 122.901 |
| 2015-07-11 | 2015 | 27 | 122.721 | 122.844 | 122.654 | 122.792 | 122.780 | 122.893 | 122.780 | 122.893 |
| 2015-07-18 | 2015 | 28 | 124.075 | 124.088 | 124.020 | 124.054 | 124.103 | 124.126 | 124.070 | 124.078 |
| 2015-07-25 | 2015 | 29 | 123.800 | 123.800 | 123.769 | 123.769 | 123.832 | 123.856 | 123.832 | 123.848 |
| 2015-08-01 | 2015 | 30 | 123.875 | 123.875 | 123.836 | 123.836 | 123.944 | 123.944 | 123.944 | 123.944 |
| 2015-08-08 | 2015 | 31 | 124.211 | 124.213 | 124.202 | 124.202 | 124.228 | 124.233 | 124.224 | 124.224 |
| 2015-08-15 | 2015 | 32 | 124.315 | 124.316 | 124.314 | 124.314 | 124.337 | 124.340 | 124.337 | 124.340 |
| 2015-08-22 | 2015 | 33 | 122.052 | 122.052 | 122.023 | 122.023 | 122.064 | 122.106 | 122.064 | 122.106 |
| 2015-08-29 | 2015 | 34 | 121.736 | 121.736 | 121.682 | 121.696 | 121.750 | 121.788 | 121.750 | 121.775 |
| 2015-09-05 | 2015 | 35 | 119.030 | 119.030 | 119.009 | 119.026 | 119.036 | 119.055 | 119.029 | 119.055 |
| 2015-09-12 | 2015 | 36 | 120.582 | 120.582 | 120.574 | 120.574 | 120.595 | 120.595 | 120.587 | 120.587 |
| 2015-09-19 | 2015 | 37 | 119.942 | 119.959 | 119.919 | 119.955 | 119.991 | 120.046 | 119.991 | 120.036 |
| 2015-09-26 | 2015 | 38 | 120.574 | 120.574 | 120.544 | 120.544 | 120.610 | 120.645 | 120.610 | 120.623 |
| 2015-10-03 | 2015 | 39 | 119.860 | 119.875 | 119.860 | 119.875 | 119.945 | 119.954 | 119.945 | 119.954 |
| 2015-10-10 | 2015 | 40 | 120.208 | 120.208 | 120.189 | 120.189 | 120.244 | 120.278 | 120.244 | 120.278 |
| 2015-10-17 | 2015 | 41 | 119.436 | 119.436 | 119.407 | 119.407 | 119.476 | 119.498 | 119.476 | 119.489 |
| 2015-10-24 | 2015 | 42 | 121.422 | 121.422 | 121.419 | 121.419 | 121.498 | 121.501 | 121.498 | 121.501 |
| 2015-10-31 | 2015 | 43 | 120.594 | 120.594 | 120.584 | 120.584 | 120.630 | 120.666 | 120.630 | 120.666 |
| 2015-11-07 | 2015 | 44 | 123.128 | 123.169 | 123.117 | 123.119 | 123.199 | 123.226 | 123.199 | 123.226 |
| 2015-11-14 | 2015 | 45 | 122.576 | 122.579 | 122.564 | 122.579 | 122.655 | 122.658 | 122.646 | 122.658 |
| 2015-11-21 | 2015 | 46 | 122.768 | 122.768 | 122.752 | 122.752 | 122.810 | 122.831 | 122.810 | 122.831 |
| 2015-11-28 | 2015 | 47 | 122.722 | 122.812 | 122.722 | 122.812 | 122.849 | 122.894 | 122.849 | 122.888 |
| 2015-12-05 | 2015 | 48 | 123.113 | 123.113 | 123.088 | 123.088 | 123.128 | 123.144 | 123.126 | 123.126 |
| 2015-12-12 | 2015 | 49 | 120.950 | 120.956 | 120.929 | 120.929 | 120.988 | 121.001 | 120.988 | 120.990 |
| 2015-12-19 | 2015 | 50 | 121.138 | 121.138 | 121.099 | 121.099 | 121.176 | 121.193 | 121.176 | 121.181 |
| 2015-12-26 | 2015 | 51 | 120.273 | 120.274 | 120.269 | 120.269 | 120.281 | 120.281 | 120.279 | 120.279 |
| 2016-01-02 | 2015 | 52 | 120.206 | 120.222 | 120.184 | 120.191 | 120.212 | 120.237 | 120.212 | 120.225 |
| 2016-01-09 | 2016 | 1 | 117.226 | 117.226 | 117.198 | 117.201 | 117.281 | 117.291 | 117.281 | 117.283 |
| 2016-01-16 | 2016 | 2 | 116.969 | 116.969 | 116.954 | 116.954 | 117.070 | 117.071 | 117.070 | 117.071 |
| 2016-01-23 | 2016 | 3 | 118.760 | 118.760 | 118.737 | 118.744 | 118.788 | 118.826 | 118.788 | 118.826 |
| 2016-01-30 | 2016 | 4 | 121.115 | 121.120 | 121.030 | 121.119 | 121.135 | 121.140 | 121.110 | 121.139 |
| 2016-02-06 | 2016 | 5 | 116.824 | 116.824 | 116.791 | 116.798 | 116.870 | 116.918 | 116.838 | 116.840 |
| 2016-02-13 | 2016 | 6 | 113.200 | 113.208 | 113.144 | 113.170 | 113.221 | 113.276 | 113.200 | 113.248 |
| 2016-02-20 | 2016 | 7 | 112.551 | 112.556 | 112.539 | 112.539 | 112.581 | 112.596 | 112.562 | 112.596 |
| 2016-02-27 | 2016 | 8 | 113.962 | 113.964 | 113.959 | 113.964 | 113.991 | 113.994 | 113.991 | 113.994 |
| 2016-03-05 | 2016 | 9 | 113.757 | 113.774 | 113.740 | 113.774 | 113.776 | 113.834 | 113.774 | 113.820 |
| 2016-03-12 | 2016 | 10 | 113.814 | 113.846 | 113.788 | 113.790 | 113.845 | 113.878 | 113.834 | 113.876 |
| 2016-03-19 | 2016 | 11 | 111.532 | 111.544 | 111.516 | 111.542 | 111.561 | 111.592 | 111.548 | 111.582 |
| 2016-03-26 | 2016 | 12 | 113.016 | 113.029 | 113.016 | 113.029 | 113.110 | 113.118 | 113.110 | 113.118 |
| 2016-04-02 | 2016 | 13 | 111.600 | 111.600 | 111.599 | 111.599 | 111.638 | 111.666 | 111.638 | 111.666 |
| 2016-04-09 | 2016 | 14 | 108.062 | 108.062 | 108.020 | 108.048 | 108.102 | 108.116 | 108.102 | 108.104 |
| 2016-04-16 | 2016 | 15 | 108.776 | 108.776 | 108.738 | 108.744 | 108.790 | 108.798 | 108.774 | 108.780 |
| 2016-04-23 | 2016 | 16 | 111.791 | 111.804 | 111.780 | 111.788 | 111.818 | 111.842 | 111.798 | 111.804 |
| 2016-04-30 | 2016 | 17 | 106.314 | 106.338 | 106.283 | 106.283 | 106.369 | 106.392 | 106.332 | 106.376 |
| 2016-05-07 | 2016 | 18 | 107.049 | 107.110 | 107.031 | 107.100 | 107.124 | 107.144 | 107.084 | 107.116 |
| 2016-05-14 | 2016 | 19 | 108.634 | 108.634 | 108.601 | 108.601 | 108.654 | 108.690 | 108.654 | 108.689 |
| 2016-05-21 | 2016 | 20 | 110.126 | 110.146 | 110.084 | 110.098 | 110.156 | 110.176 | 110.140 | 110.174 |
| 2016-05-28 | 2016 | 21 | 110.220 | 110.220 | 110.187 | 110.187 | 110.256 | 110.284 | 110.256 | 110.284 |
| 2016-06-04 | 2016 | 22 | 106.536 | 106.544 | 106.506 | 106.538 | 106.554 | 106.598 | 106.546 | 106.554 |
| 2016-06-11 | 2016 | 23 | 106.922 | 106.924 | 106.912 | 106.916 | 106.952 | 106.958 | 106.946 | 106.950 |
| 2016-06-18 | 2016 | 24 | 104.111 | 104.111 | 104.069 | 104.083 | 104.207 | 104.207 | 104.166 | 104.166 |
| 2016-06-25 | 2016 | 25 | 102.149 | 102.199 | 102.149 | 102.199 | 102.371 | 102.441 | 102.371 | 102.441 |
| 2016-07-02 | 2016 | 26 | 102.551 | 102.551 | 102.464 | 102.464 | 102.562 | 102.562 | 102.528 | 102.530 |
| 2016-07-09 | 2016 | 27 | 100.569 | 100.569 | 100.569 | 100.569 | 100.592 | 100.611 | 100.592 | 100.611 |
| 2016-07-16 | 2016 | 28 | 104.839 | 104.839 | 104.784 | 104.804 | 104.902 | 104.919 | 104.848 | 104.898 |
| 2016-07-23 | 2016 | 29 | 106.030 | 106.030 | 105.999 | 106.012 | 106.084 | 106.110 | 106.076 | 106.090 |
| 2016-07-30 | 2016 | 30 | 102.024 | 102.024 | 102.010 | 102.010 | 102.100 | 102.100 | 102.080 | 102.080 |
| 2016-08-06 | 2016 | 31 | 101.819 | 101.819 | 101.784 | 101.792 | 101.856 | 101.882 | 101.848 | 101.872 |
| 2016-08-13 | 2016 | 32 | 101.266 | 101.268 | 101.266 | 101.268 | 101.346 | 101.348 | 101.346 | 101.348 |
| 2016-08-20 | 2016 | 33 | 100.174 | 100.187 | 100.174 | 100.174 | 100.239 | 100.245 | 100.239 | 100.245 |
| 2016-08-27 | 2016 | 34 | 101.820 | 101.820 | 101.759 | 101.759 | 101.857 | 101.857 | 101.856 | 101.856 |
| 2016-09-03 | 2016 | 35 | 103.980 | 104.016 | 103.874 | 103.874 | 104.051 | 104.051 | 103.967 | 103.967 |
| 2016-09-10 | 2016 | 36 | 102.690 | 102.690 | 102.644 | 102.644 | 102.731 | 102.731 | 102.726 | 102.726 |
| 2016-09-17 | 2016 | 37 | 102.259 | 102.259 | 102.234 | 102.244 | 102.285 | 102.328 | 102.285 | 102.316 |
| 2016-09-24 | 2016 | 38 | 100.987 | 100.987 | 100.987 | 100.987 | 101.046 | 101.081 | 101.046 | 101.081 |
| 2016-10-01 | 2016 | 39 | 101.269 | 101.279 | 101.269 | 101.279 | 101.360 | 101.372 | 101.360 | 101.372 |
| 2016-10-08 | 2016 | 40 | 102.887 | 102.896 | 102.877 | 102.896 | 102.906 | 102.948 | 102.900 | 102.948 |
| 2016-10-15 | 2016 | 41 | 104.178 | 104.183 | 104.178 | 104.183 | 104.217 | 104.218 | 104.217 | 104.218 |
| 2016-10-22 | 2016 | 42 | 103.820 | 103.824 | 103.820 | 103.822 | 103.836 | 103.875 | 103.836 | 103.838 |
| 2016-10-29 | 2016 | 43 | 104.710 | 104.710 | 104.665 | 104.665 | 104.720 | 104.755 | 104.720 | 104.755 |
| 2016-11-05 | 2016 | 44 | 103.072 | 103.099 | 103.049 | 103.099 | 103.124 | 103.149 | 103.124 | 103.146 |
| 2016-11-12 | 2016 | 45 | 106.615 | 106.638 | 106.590 | 106.590 | 106.658 | 106.659 | 106.647 | 106.652 |
| 2016-11-19 | 2016 | 46 | 110.922 | 110.922 | 110.859 | 110.859 | 110.934 | 110.951 | 110.920 | 110.951 |
| 2016-11-26 | 2016 | 47 | 112.942 | 113.204 | 112.942 | 113.163 | 113.040 | 113.258 | 113.040 | 113.254 |
| 2016-12-03 | 2016 | 48 | 113.489 | 113.489 | 113.489 | 113.489 | 113.532 | 113.551 | 113.532 | 113.551 |
| 2016-12-10 | 2016 | 49 | 115.177 | 115.177 | 115.159 | 115.159 | 115.238 | 115.242 | 115.238 | 115.242 |
| 2016-12-17 | 2016 | 50 | 117.990 | 117.990 | 117.905 | 117.905 | 118.009 | 118.011 | 117.972 | 117.976 |
| 2016-12-24 | 2016 | 51 | 117.277 | 117.277 | 117.238 | 117.242 | 117.372 | 117.372 | 117.314 | 117.322 |
| 2017-01-01 | 2016 | 52 | 116.994 | 117.004 | 116.978 | 116.978 | 117.083 | 117.096 | 117.076 | 117.076 |
| 2017-01-08 | 2017 | 1 | 116.928 | 116.928 | 116.899 | 116.899 | 116.944 | 116.958 | 116.941 | 116.947 |
| 2017-01-14 | 2017 | 2 | 114.447 | 114.506 | 114.427 | 114.427 | 114.511 | 114.536 | 114.511 | 114.518 |
| 2017-01-21 | 2017 | 3 | 114.569 | 114.569 | 114.569 | 114.569 | 114.640 | 114.665 | 114.640 | 114.665 |
| 2017-01-28 | 2017 | 4 | 115.060 | 115.076 | 115.059 | 115.068 | 115.110 | 115.126 | 115.102 | 115.120 |
| 2017-02-04 | 2017 | 5 | 112.564 | 112.570 | 112.542 | 112.552 | 112.572 | 112.606 | 112.568 | 112.581 |
| 2017-02-11 | 2017 | 6 | 113.212 | 113.243 | 113.202 | 113.222 | 113.279 | 113.317 | 113.275 | 113.308 |
| 2017-02-18 | 2017 | 7 | 112.885 | 112.900 | 112.878 | 112.896 | 112.899 | 112.922 | 112.899 | 112.916 |
| 2017-02-25 | 2017 | 8 | 112.130 | 112.164 | 112.103 | 112.145 | 112.190 | 112.219 | 112.187 | 112.193 |
| 2017-03-04 | 2017 | 9 | 114.013 | 114.034 | 113.995 | 114.023 | 114.057 | 114.104 | 114.057 | 114.061 |
| 2017-03-11 | 2017 | 10 | 114.799 | 114.813 | 114.763 | 114.778 | 114.876 | 114.883 | 114.828 | 114.836 |
| 2017-03-18 | 2017 | 11 | 112.702 | 112.710 | 112.678 | 112.682 | 112.738 | 112.763 | 112.719 | 112.733 |
| 2017-03-25 | 2017 | 12 | 111.248 | 111.314 | 111.222 | 111.312 | 111.291 | 111.366 | 111.273 | 111.357 |
| 2017-04-01 | 2017 | 13 | 111.372 | 111.378 | 111.346 | 111.363 | 111.401 | 111.419 | 111.397 | 111.408 |
| 2017-04-08 | 2017 | 14 | 111.085 | 111.085 | 111.054 | 111.054 | 111.118 | 111.139 | 111.118 | 111.139 |
| 2017-04-15 | 2017 | 15 | 108.585 | 108.592 | 108.560 | 108.565 | 108.681 | 108.687 | 108.629 | 108.641 |
| 2017-04-22 | 2017 | 16 | 109.008 | 109.008 | 108.951 | 108.951 | 109.084 | 109.084 | 109.049 | 109.049 |
| 2017-04-29 | 2017 | 17 | 111.512 | 111.512 | 111.510 | 111.510 | 111.537 | 111.537 | 111.537 | 111.537 |
| 2017-05-06 | 2017 | 18 | 112.687 | 112.687 | 112.618 | 112.638 | 112.776 | 112.776 | 112.701 | 112.728 |
| 2017-05-13 | 2017 | 19 | 113.335 | 113.335 | 113.335 | 113.335 | 113.360 | 113.362 | 113.360 | 113.362 |
| 2017-05-20 | 2017 | 20 | 111.271 | 111.271 | 111.241 | 111.262 | 111.293 | 111.300 | 111.280 | 111.281 |
| 2017-05-27 | 2017 | 21 | 111.312 | 111.320 | 111.304 | 111.309 | 111.336 | 111.345 | 111.323 | 111.323 |
| 2017-06-03 | 2017 | 22 | 110.428 | 110.460 | 110.422 | 110.438 | 110.441 | 110.468 | 110.439 | 110.453 |
| 2017-06-10 | 2017 | 23 | 110.321 | 110.321 | 110.316 | 110.316 | 110.334 | 110.351 | 110.334 | 110.351 |
| 2017-06-17 | 2017 | 24 | 110.864 | 110.869 | 110.861 | 110.865 | 110.881 | 110.892 | 110.878 | 110.882 |
| 2017-06-24 | 2017 | 25 | 111.284 | 111.290 | 111.283 | 111.290 | 111.298 | 111.307 | 111.298 | 111.307 |
| 2017-07-01 | 2017 | 26 | 112.399 | 112.399 | 112.376 | 112.376 | 112.430 | 112.450 | 112.430 | 112.450 |
| 2017-07-08 | 2017 | 27 | 113.904 | 113.904 | 113.900 | 113.904 | 113.922 | 113.922 | 113.917 | 113.921 |
| 2017-07-15 | 2017 | 28 | 112.527 | 112.527 | 112.515 | 112.515 | 112.544 | 112.557 | 112.544 | 112.557 |
| 2017-07-22 | 2017 | 29 | 111.134 | 111.134 | 111.115 | 111.121 | 111.147 | 111.148 | 111.133 | 111.134 |
| 2017-07-29 | 2017 | 30 | 110.698 | 110.705 | 110.680 | 110.699 | 110.710 | 110.726 | 110.709 | 110.710 |
| 2017-08-05 | 2017 | 31 | 110.677 | 110.684 | 110.675 | 110.682 | 110.692 | 110.698 | 110.688 | 110.696 |
| 2017-08-12 | 2017 | 32 | 109.149 | 109.172 | 109.147 | 109.172 | 109.162 | 109.215 | 109.159 | 109.193 |
| 2017-08-19 | 2017 | 33 | 109.189 | 109.201 | 109.169 | 109.199 | 109.207 | 109.221 | 109.203 | 109.212 |
| 2017-08-26 | 2017 | 34 | 109.322 | 109.322 | 109.320 | 109.322 | 109.364 | 109.364 | 109.362 | 109.364 |
| 2017-09-02 | 2017 | 35 | 110.234 | 110.236 | 110.228 | 110.228 | 110.276 | 110.282 | 110.276 | 110.280 |
| 2017-09-09 | 2017 | 36 | 107.838 | 107.838 | 107.832 | 107.836 | 107.860 | 107.864 | 107.856 | 107.858 |
| 2017-09-16 | 2017 | 37 | 110.828 | 110.830 | 110.828 | 110.830 | 110.860 | 110.862 | 110.860 | 110.862 |
| 2017-09-23 | 2017 | 38 | 111.992 | 111.992 | 111.990 | 111.990 | 112.000 | 112.000 | 112.000 | 112.000 |
| 2017-09-30 | 2017 | 39 | 112.499 | 112.499 | 112.460 | 112.464 | 112.529 | 112.562 | 112.524 | 112.562 |
| 2017-10-07 | 2017 | 40 | 112.606 | 112.608 | 112.600 | 112.600 | 112.682 | 112.686 | 112.682 | 112.686 |
| 2017-10-14 | 2017 | 41 | 111.834 | 111.834 | 111.826 | 111.826 | 111.876 | 111.880 | 111.876 | 111.878 |
| 2017-10-21 | 2017 | 42 | 113.516 | 113.518 | 113.503 | 113.508 | 113.536 | 113.557 | 113.534 | 113.551 |
| 2017-10-28 | 2017 | 43 | 113.660 | 113.662 | 113.635 | 113.635 | 113.704 | 113.715 | 113.702 | 113.715 |
| 2017-11-04 | 2017 | 44 | 114.048 | 114.048 | 114.042 | 114.042 | 114.087 | 114.091 | 114.085 | 114.085 |
| 2017-11-11 | 2017 | 45 | 113.522 | 113.522 | 113.505 | 113.505 | 113.542 | 113.564 | 113.542 | 113.548 |
| 2017-11-18 | 2017 | 46 | 112.130 | 112.142 | 112.085 | 112.085 | 112.166 | 112.188 | 112.150 | 112.164 |
| 2017-11-25 | 2017 | 47 | 111.502 | 111.502 | 111.492 | 111.501 | 111.545 | 111.545 | 111.535 | 111.544 |
| 2017-12-02 | 2017 | 48 | 112.164 | 112.164 | 112.162 | 112.164 | 112.216 | 112.216 | 112.216 | 112.216 |
| 2017-12-09 | 2017 | 49 | 113.464 | 113.466 | 113.444 | 113.448 | 113.474 | 113.504 | 113.474 | 113.498 |
| 2017-12-16 | 2017 | 50 | 112.584 | 112.590 | 112.578 | 112.581 | 112.654 | 112.660 | 112.648 | 112.657 |
| 2017-12-23 | 2017 | 51 | 113.254 | 113.265 | 113.254 | 113.265 | 113.328 | 113.343 | 113.328 | 113.343 |
| 2017-12-31 | 2017 | 52 | 112.660 | 112.660 | 112.643 | 112.651 | 112.700 | 112.729 | 112.700 | 112.729 |
| 2018-01-07 | 2017 | 53 | NA | NA | NA | NA | NA | NA | NA | NA |
| 2018-01-07 | 2018 | 1 | 113.032 | 113.032 | 113.018 | 113.018 | 113.092 | 113.100 | 113.090 | 113.098 |
| 2018-01-13 | 2018 | 2 | 111.002 | 111.006 | 110.988 | 110.996 | 111.044 | 111.060 | 111.026 | 111.052 |
| 2018-01-20 | 2018 | 3 | 110.814 | 110.814 | 110.814 | 110.814 | 110.856 | 110.856 | 110.854 | 110.854 |
| 2018-01-27 | 2018 | 4 | 108.624 | 108.626 | 108.589 | 108.589 | 108.634 | 108.648 | 108.632 | 108.632 |
| 2018-02-03 | 2018 | 5 | 110.153 | 110.153 | 110.152 | 110.152 | 110.195 | 110.195 | 110.195 | 110.195 |
| 2018-02-10 | 2018 | 6 | 108.780 | 108.780 | 108.768 | 108.770 | 108.812 | 108.824 | 108.812 | 108.824 |
| 2018-02-17 | 2018 | 7 | 106.300 | 106.300 | 106.272 | 106.272 | 106.312 | 106.325 | 106.303 | 106.315 |
| 2018-02-24 | 2018 | 8 | 106.863 | 106.863 | 106.858 | 106.858 | 106.919 | 106.919 | 106.914 | 106.914 |
| 2018-03-03 | 2018 | 9 | 105.722 | 105.722 | 105.696 | 105.712 | 105.730 | 105.762 | 105.730 | 105.757 |
| 2018-03-10 | 2018 | 10 | 106.807 | 106.818 | 106.807 | 106.814 | 106.850 | 106.850 | 106.822 | 106.822 |
| 2018-03-17 | 2018 | 11 | 105.964 | 105.966 | 105.953 | 105.953 | 106.001 | 106.007 | 106.001 | 106.007 |
| 2018-03-24 | 2018 | 12 | 104.728 | 104.730 | 104.708 | 104.712 | 104.744 | 104.766 | 104.742 | 104.766 |
| 2018-03-31 | 2018 | 13 | 106.261 | 106.261 | 106.258 | 106.260 | 106.312 | 106.312 | 106.312 | 106.312 |
| 2018-04-07 | 2018 | 14 | 106.926 | 106.926 | 106.913 | 106.915 | 106.950 | 106.962 | 106.950 | 106.962 |
| 2018-04-14 | 2018 | 15 | 107.334 | 107.338 | 107.334 | 107.338 | 107.377 | 107.385 | 107.377 | 107.385 |
| 2018-04-21 | 2018 | 16 | 107.628 | 107.628 | 107.616 | 107.616 | 107.656 | 107.674 | 107.656 | 107.674 |
| 2018-04-28 | 2018 | 17 | 109.042 | 109.046 | 109.022 | 109.022 | 109.074 | 109.088 | 109.064 | 109.080 |
| 2018-05-05 | 2018 | 18 | 109.055 | 109.059 | 109.055 | 109.056 | 109.098 | 109.105 | 109.098 | 109.105 |
| 2018-05-12 | 2018 | 19 | 109.360 | 109.360 | 109.358 | 109.358 | 109.412 | 109.412 | 109.410 | 109.410 |
| 2018-05-19 | 2018 | 20 | 110.746 | 110.746 | 110.730 | 110.736 | 110.760 | 110.789 | 110.760 | 110.783 |
| 2018-05-26 | 2018 | 21 | 109.378 | 109.380 | 109.362 | 109.362 | 109.398 | 109.409 | 109.398 | 109.409 |
| 2018-06-02 | 2018 | 22 | 109.514 | 109.514 | 109.488 | 109.488 | 109.524 | 109.548 | 109.524 | 109.535 |
| 2018-06-09 | 2018 | 23 | 109.511 | 109.536 | 109.507 | 109.509 | 109.554 | 109.558 | 109.550 | 109.554 |
| 2018-06-16 | 2018 | 24 | 110.644 | 110.650 | 110.644 | 110.644 | 110.687 | 110.692 | 110.687 | 110.691 |
| 2018-06-23 | 2018 | 25 | 109.982 | 109.984 | 109.976 | 109.976 | 109.992 | 109.994 | 109.984 | 109.984 |
| 2018-06-30 | 2018 | 26 | 110.678 | 110.678 | 110.666 | 110.666 | 110.698 | 110.708 | 110.698 | 110.708 |
| 2018-07-07 | 2018 | 27 | 110.450 | 110.454 | 110.446 | 110.449 | 110.477 | 110.499 | 110.477 | 110.499 |
## Tidy dataset for modelling.
data_m1 %<>%
mutate(open = (BidOpen + AskOpen)/2, close = (BidClose + AskClose)/2) %>%
dplyr::rename(high = BidHigh, low = AskLow) %>% #use bid price for sell.
dplyr::select(index, open, high, low, close) # and ask price for buy.Here I try to check if the filled dataset bias or not. Due to above I used open = (BidOpen + AskOpen)/2, high = BidHigh, low = AskLow and close = (BidClose + AskClose)/21. There will probably have bias.
tb3 <- data_m1 %>% mutate(
bias.open = if_else(open>high|open<low, 1, 0),
bias.high = if_else(high<open|high<low|high<close, 1, 0),
bias.low = if_else(low>open|low>high|low>close, 1, 0),
bias.close = if_else(close>high|close<low, 1, 0)) %>%
dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)# %>%
# kable(caption = 'Bias Imputation') %>%
# kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
# scroll_box(width = '100%', height = '400px')
tb3## # A tibble: 709,076 x 9
## index open high low close bias.open bias.high bias.low
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-05 00:01:00 121. 121. 121. 121. 1 1 1
## 2 2015-01-05 00:02:00 121. 121. 121. 121. 1 1 1
## 3 2015-01-05 00:04:00 121. 121. 121. 121. 1 1 0
## 4 2015-01-05 00:05:00 121. 121. 121. 121. 1 1 0
## 5 2015-01-05 00:09:00 121. 121. 121. 121. 0 0 1
## 6 2015-01-05 00:10:00 121. 121. 121. 121. 1 1 1
## 7 2015-01-05 00:11:00 121. 121. 121. 121. 1 1 1
## 8 2015-01-05 00:12:00 121. 121. 121. 121. 1 1 1
## 9 2015-01-05 00:13:00 121. 121. 121. 121. 1 1 1
## 10 2015-01-05 00:14:00 121. 121. 121. 121. 0 0 1
## # ... with 709,066 more rows, and 1 more variable: bias.close <dbl># -------- eval=FALSE -----------
## Below prove that the dataset has no any bias or error.
> read_rds(paste0(dtr1, '/data_m1.rds')) %>% mutate(
+ open = BidOpen, high = BidHigh, low = BidLow, close = BidClose,
+ bias.open = if_else(open>high|open<low, 1, 0),
+ bias.high = if_else(high<open|high<low|high<close, 1, 0),
+ bias.low = if_else(low>open|low>high|low>close, 1, 0),
+ bias.close = if_else(close>high|close<low, 1, 0)) %>%
+ dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)
# A tibble: 0 x 19
# ... with 19 variables: index <dttm>, year <dbl>, week <dbl>, BidOpen <dbl>, BidHigh <dbl>, BidLow <dbl>,
# BidClose <dbl>, AskOpen <dbl>, AskHigh <dbl>, AskLow <dbl>, AskClose <dbl>, open <dbl>, high <dbl>, low <dbl>,
# close <dbl>, bias.open <dbl>, bias.high <dbl>, bias.low <dbl>, bias.close <dbl>
> read_rds(paste0(dtr, '/data_tm1.rds')) %>% mutate(
+ open = BidOpen, high = BidHigh, low = BidLow, close = BidClose,
+ bias.open = if_else(open>high|open<low, 1, 0),
+ bias.high = if_else(high<open|high<low|high<close, 1, 0),
+ bias.low = if_else(low>open|low>high|low>close, 1, 0),
+ bias.close = if_else(close>high|close<low, 1, 0)) %>%
+ dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)
# A tibble: 0 x 19
# ... with 19 variables: index <dttm>, year <dbl>, week <dbl>, AskOpen <dbl>, AskHigh <dbl>, AskLow <dbl>,
# AskClose <dbl>, BidOpen <dbl>, BidHigh <dbl>, BidLow <dbl>, BidClose <dbl>, open <dbl>, high <dbl>, low <dbl>,
# close <dbl>, bias.open <dbl>, bias.high <dbl>, bias.low <dbl>, bias.close <dbl>
> read_rds(paste0(dtr1, '/data_m1.rds')) %>% mutate(
+ open = AskOpen, high = AskHigh, low = AskLow, close = AskClose,
+ bias.open = if_else(open>high|open<low, 1, 0),
+ bias.high = if_else(high<open|high<low|high<close, 1, 0),
+ bias.low = if_else(low>open|low>high|low>close, 1, 0),
+ bias.close = if_else(close>high|close<low, 1, 0)) %>%
+ dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)
# A tibble: 0 x 19
# ... with 19 variables: index <dttm>, year <dbl>, week <dbl>, BidOpen <dbl>, BidHigh <dbl>, BidLow <dbl>,
# BidClose <dbl>, AskOpen <dbl>, AskHigh <dbl>, AskLow <dbl>, AskClose <dbl>, open <dbl>, high <dbl>, low <dbl>,
# close <dbl>, bias.open <dbl>, bias.high <dbl>, bias.low <dbl>, bias.close <dbl>
> read_rds(dtr1, paste0('/data_tm1.rds')) %>% mutate(
+ open = AskOpen, high = AskHigh, low = AskLow, close = AskClose,
+ bias.open = if_else(open>high|open<low, 1, 0),
+ bias.high = if_else(high<open|high<low|high<close, 1, 0),
+ bias.low = if_else(low>open|low>high|low>close, 1, 0),
+ bias.close = if_else(close>high|close<low, 1, 0)) %>%
+ dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)
# A tibble: 0 x 19
# ... with 19 variables: index <dttm>, year <dbl>, week <dbl>, AskOpen <dbl>, AskHigh <dbl>, AskLow <dbl>,
# AskClose <dbl>, BidOpen <dbl>, BidHigh <dbl>, BidLow <dbl>, BidClose <dbl>, open <dbl>, high <dbl>, low <dbl>,
# close <dbl>, bias.open <dbl>, bias.high <dbl>, bias.low <dbl>, bias.close <dbl>I initially try to use bid for high and ask for low in order to produce a better prediction price for buy and sell. However, I use the mean value of OHLC all prices for this paper to avoid the statistical error/bias.
Due to 1min dataset is better than (more complete) tickdata-to-1min, here I use the 1min dataset.
if(!exists('data_m1')) {
data_m1 <- read_rds(paste0(dtr1s, '/data_m1.rds'))
}
if(names(data_m1) %>% str_detect('Bid|Ask') %>% any()) {
data_m1 %<>%
mutate(open = (BidOpen + AskOpen)/2,
high = (BidHigh + AskHigh)/2,
low = (BidLow + AskLow)/2,
close = (BidClose + AskClose)/2) %>%
dplyr::select(index, open, high, low, close)
}tb4 <- data_m1 %>% mutate(
bias.open = if_else(open>high|open<low, 1, 0),
bias.high = if_else(high<open|high<low|high<close, 1, 0),
bias.low = if_else(low>open|low>high|low>close, 1, 0),
bias.close = if_else(close>high|close<low, 1, 0)) %>%
dplyr::filter(bias.open==1|bias.high==1|bias.low==1|bias.close==1)# %>%
# kable(caption = 'Bias Imputation') %>%
# kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
# scroll_box(width = '100%', height = '400px')
tb4## # A tibble: 709,076 x 9
## index open high low close bias.open bias.high bias.low
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-05 00:01:00 121. 121. 121. 121. 1 1 1
## 2 2015-01-05 00:02:00 121. 121. 121. 121. 1 1 1
## 3 2015-01-05 00:04:00 121. 121. 121. 121. 1 1 0
## 4 2015-01-05 00:05:00 121. 121. 121. 121. 1 1 0
## 5 2015-01-05 00:09:00 121. 121. 121. 121. 0 0 1
## 6 2015-01-05 00:10:00 121. 121. 121. 121. 1 1 1
## 7 2015-01-05 00:11:00 121. 121. 121. 121. 1 1 1
## 8 2015-01-05 00:12:00 121. 121. 121. 121. 1 1 1
## 9 2015-01-05 00:13:00 121. 121. 121. 121. 1 1 1
## 10 2015-01-05 00:14:00 121. 121. 121. 121. 0 0 1
## # ... with 709,066 more rows, and 1 more variable: bias.close <dbl>//<script type="text/javascript" src="//cdn.datacamp.com/dcl-react.js.gz"></script>Source : DataCamp Light
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4 Modelling
4.1 Seasonal Modelling
Below articles introduce TBATS models tbats() and Dynamic harmonic regression with multiple seasonal periods auto.arima(). Here I also includes ts(), MIDAS midasr(), GARCH-MIDAS, mcsGARCH and Levy Process for this research.
- Forecasting: Principles and Practice - 11.1 Complex seasonality
- Forecasting: Principles and Practice - 12.1 Weekly, daily and sub-daily data
Progress Function
task_progress <- function(mbase, timeID0 = NULL, scs = 60, .pattern = '^mts|^sets', .loops = TRUE) {
## ------------- 定时查询进度 ----------------------
## 每分钟自动查询与更新以上模拟预测汇价进度（储存文件量）。
require('magrittr')
require('tibble')
if(!is.data.frame(class(mbase))) {
mbase %<>% data.frame
}
if (.loops == TRUE) {
while(1) {
cat('Current Tokyo Time :', as.character(now('Asia/Tokyo')), '\n\n')
y = as_date(mbase$index) %>%
unique
y <- y[weekdays(y) != 'Saturday'] #filter and omit the weekly last price which is 12:00am on saturday
datee = y
if(is.null(timeID0)) {
timeID0 = y[1]
} else if (is.Date(timeID0)) {
timeID0 = as_date(timeID0)
} else {
timeID0 = as_date(mbase$index) %>%
unique
}
y = y[y >= timeID0]
x = list.files(paste0('./data/fx/USDJPY/'), pattern = .pattern) %>%
str_replace_all('.rds', '') %>%
str_replace_all('.201', '_201') %>%
str_split_fixed('_', '2') %>%
as_tibble %>%
dplyr::rename('Model' = 'V1', 'Date' = 'V2') %>%
mutate(Model = factor(Model), Date = as_date(Date))
x = join(tibble(Date = datee), x) %>%
as_tibble
x %<>% na.omit
x %<>% mutate(binary = if_else(is.na(Model), 0, 1)) %>%
spread(Model, binary)
z <- ldply(x[,-1], function(zz) {
na.omit(zz) %>% length }) %>%
dplyr::rename(x = V1) %>%
mutate(n = length(y), progress = percent(x/n))
print(z)
prg = sum(z$x)/sum(z$n)
cat('\n================', as.character(percent(prg)), '================\n\n')
if (prg == 1) break #倘若进度达到100%就停止更新。
Sys.sleep(scs) #以上ldply()耗时3~5秒，而休息时间60秒。
}
} else {
cat('Current Tokyo Time :', as.character(now('Asia/Tokyo')), '\n\n')
y = as_date(mbase$index) %>%
unique
datee = y
if(is.null(timeID0)) {
timeID0 = y[1]
} else if (is.Date(timeID0)) {
timeID0 = as_date(timeID0)
} else {
timeID0 = as_date(mbase$index) %>%
unique
}
y = y[y >= timeID0]
x = list.files(paste0('./data/fx/USDJPY/'), pattern = .pattern) %>%
str_replace_all('.rds', '') %>%
str_replace_all('.201', '_201') %>%
str_split_fixed('_', '2') %>%
as_tibble %>%
dplyr::rename('Model' = 'V1', 'Date' = 'V2') %>%
mutate(Model = factor(Model), Date = as_date(Date))
x = join(tibble(Date = datee), x) %>%
as_tibble
x %<>% na.omit
x %<>% mutate(binary = if_else(is.na(Model), 0, 1)) %>%
spread(Model, binary)
z <- ldply(x[,-1], function(zz) {
na.omit(zz) %>% length }) %>%
dplyr::rename(x = V1) %>%
mutate(n = length(y), progress = percent(x/n))
print(z)
prg = sum(z$x)/sum(z$n)
cat('\n================', as.character(percent(prg)), '================\n\n')
}
}4.2 Seasonal ETS
4.2.1 ETS ts()
The forecast.ets() will automatically use the optimal ets() which is similar theory with auto.arima().
4.2.2 Weekly >> Daily
I set the length of dataset as weekly but the frequency set as 1440 minutes (per day).
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h = 1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.3 Monthly >> Daily
I set the length of dataset as monthly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a monthly dataset.
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.mo.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.mo.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.4 Quarterly >> Daily
I set the length of dataset as quarterly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a quarterly dataset.
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.qt.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.qt.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.5 Yearly >> Daily
I set the length of dataset as yearly but the frequency set as 1440 minutes (per day). Initial forecast will be based on weekly dataset and then accumulated date-by-date until a yearly dataset.
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>% tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 1440) %>%
forecast(h=1440) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.yr.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.yr.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.6 Weekly >> Weekly
I set the length of dataset as weekly but the frequency set as 7200 minutes (per week).
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.wk.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.wk.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.7 Monthly >> Weekly
I set the length of dataset as monthly but the frequency set as 7200 minutes (per week).
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.mo.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.mo.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.8 Quarterly >> Weekly
I set the length of dataset as quarterly but the frequency set as 7200 minutes (per week).
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.qt.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.qt.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.2.9 Yearly >> Weekly
I set the length of dataset as yearly but the frequency set as 7200 minutes (per week).
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 7200)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
sets <- smp %>%
tk_ts(frequency = 7200) %>%
forecast(h = 7200) %>%
llply(tk_tbl)
if(is.double(sets$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
sets$forecast$index <- sq
} else {
sets$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 7200)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.yr.7200.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.yr.7200.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.3 Seasonal ARIMA
4.3.1 Introduce SARIMA
- Seasonal model with auto.arima
- Seasonality not taken account of in
auto.arima()ask about why there has no - 8.5 Non-seasonal ARIMA models introduce a non-seasonal ARIMA model.
- 8.9 Seasonal ARIMA models introduce the arima and also sarima models, teach we how to get the
P,D,Q. - Seasonality in
auto.arima()from forecast package ask the question which is what I am trying to know (normal arima model only get(p,d,q)but not(P,D,Q)). The answer is do NOT set bothapproximationandstepwisetoFALSE. - Is there a way to force seasonality from
auto.arimaask about how to model a force-seasonal-ARIMA. The topic talk about theDparameter inauto.arimawhich governs seasonal differencing. The example shows thatD=1will get a smaller AIC/BIC figures than defaultD=NULL. - Why does
auto.arimadrop my seasonality component whenstepwise=FALSEandapproximation=FALSEask about why thestepwise=FALSEandapproximation=FALSEgot the better AIC than default model. The answer describe that normallymax.order=5where we can get a better truly seasonal model, just increase themax.order=10. There is not too much gained usingapproximation=FALSE. What that does is force it to evaluate the likelihood more accurately for each model, but the approximation is quite good and much faster, so is usually acceptable. - How to read p,d and q of
auto.arima()? ask about what is the meaning ofa$armaand somebody answer the help page inauto.arima()has descibe thata$armais(p, q, P, Q, s, d, D). - In R,
auto.arimafails to capture seasonality simulate an annual dataset with settrace=TRUE,stepwise=FALSEandD=1but didn’t provides the answer to get optimalP,D,Q. - How I can get best arima model in R (closed) only say the
auto.arima()able get the best model, however does not provides the answer how to get the optimalP,D,Qinstead of onlyp,d,q. - how to extract integration order (d) from auto.arima ask that the
ndiffs()sometimes give the different resukt than best model, describe thea$arma. More generally, the order(d)is the next to last element; the seasonal order(D)is the last. Soa$arma[length(a$arma)-1]is the order d anda$arma[length(a$arma)]is the seasonal order. - How to read p,d and q of
auto.arima()? describe the help page inauto.arima()has descibe thata$armais(p, q, P, Q, d, D). - How to interpret the second part of an auto arima result in R? interpret the seasonal arima model.
- extract ARIMA specificaiton provides a function how to extract the
a$arma[c(1, 6, 2, 3, 7, 4, 5)]from anauto.arima(). - How to include seasonality in auto arima with regressors in R? use a
xregfor seasonal model. - Step-by-Step Graphic Guide to Forecasting through ARIMA Modeling using R – Manufacturing Case Study Example (Part 4) forecast seasonal sales by using
auto.arima(). - Frequency parameter and its impact on auto.arima results2 ask about the determination of frequency parameter for
seasonal periodwhere the author offorecastpackage provides a details and concise answer. auto.arimaWarnsNaNsProduced on Std Error suggested setstepwise=FALSEandapproximation=FALSEis better model.
If you look at the help file of auto.arima and navigate to the section “Value”, you are directed to the help file of arima function and there you find the following (under the section “Value”) regarding the arma slot: A compact form of the specification, as a vector giving the number of AR, MA, seasonal AR and seasonal MA coefficients, plus the period and the number of non-seasonal and seasonal differences. That is what the seven elements you reported correspond to. In your case, you have a non-seasonal
ARIMA(1,2,0).
Source : How to read p,d and q of auto.arima()? (which is 1 among the reference link above.)
So far, we have restricted our attention to non-seasonal data and non-seasonal ARIMA models. However, ARIMA models are also capable of modelling a wide range of seasonal data. A seasonal ARIMA model is formed by including additional seasonal terms in the ARIMA models we have seen so far. It is written as follows:
| ARIMA | \(\underbrace{(p, d, q)}\) | \(\underbrace{(P, D, Q)_{m}}\) |
|---|---|---|
| ↑ | ↑ | |
| Non-seasonal part of the model | Seasonal part of the model |
where m = number of observations per year. We use uppercase notation for the seasonal parts of the model, and lowercase notation for the non-seasonal parts of the model.
The seasonal part of the model consists of terms that are similar to the non-seasonal components of the model, but involve backshifts of the seasonal period. For example, an \(ARIMA(1,1,1)(1,1,1)_{4}\) model (without a constant) is for quarterly data (m = 4), and can be written as
\[(1 - {\color{Red}\phi_{1}}B)~(1 - {\color{Red}\Phi_{1}}B^{4}) (1 - B) (1 - B^{4})y_{t} = (1 + {\color{Red}\theta_{1}}B)~ (1 + {\color{Red}\Theta_{1}}B^{4})\varepsilon_{t}\]
The additional seasonal terms are simply multiplied by the non-seasonal terms.
auto.arima(euretail, stepwise=FALSE, approximation=FALSE) is better than auto.arima(euretail).
The
auto.arima()function usesnsdiffs()to determine D (the number of seasonal differences to use), andndiffs()to determine d (the number of ordinary differences to use). The selection of the other model parameters(p, q, P and Q)are all determined by minimizing the AICc, as with non-seasonal ARIMA models.
Source : 8.9 Seasonal ARIMA models (which is 1 among the reference link above.)
Above 8.5 Non-seasonal ARIMA models reference link describe the auto.arima() and the default setting is seasonal=TRUE where it will automatically model3 .
The default arguments are designed for rapid estimation of models for many time series. If you are analysing just one time series, and can afford to take some more time, it is recommended that you set stepwise=FALSE and approximation=FALSE. Non-stepwise selection can be slow, especially for seasonal data. The stepwise algorithm outlined in Hyndman & Khandakar (2008) is used except that the default method for selecting seasonal differences is now based on an estimate of seasonal strength (Wang, Smith & Hyndman, 2006) rather than the Canova-Hansen test. There are also some other minor variations to the algorithm described in Hyndman and Khandakar (2008).
Source : help section of auto.arima().
ARIMA(2,1,1)(1,0,0)[12]is seasonal ARIMA.[12]stands for number of periods in season, i.e. months in year in this case.(1,0,0)stands for seasonal part of model. Take a look at this.
Source : extract ARIMA specificaiton (which is 1 among the reference link above.)
You can force a seasonal model by setting
D=1, althoughauto.arima()runs for quite some time with forced seasonality. (Note that the information criteria are not comparable between the original and the differenced series.) \[ \begin{array}{l,l,l} &\text{Training} & \text{Test}\\ \mathrm{ARIMA}(2,1,1) & 5.729 & 7.657\\ \mathrm{SARIMA}(1,1,0)_{52}\text{ with drift} & 6.481 & 7.390\\ \text{3 harmonics, }\mathrm{ARIMA}(2,1,0) & 5.578 & 5.151\\ \text{4 harmonics, }\mathrm{ARIMA}(2,1,1) & 5.219 & 5.188 \end{array} \]
Source : Seasonality not taken account of in auto.arima() (which is 1 among the reference link above.)
The problem with fitting seasonal ARIMA to daily data is that the “seasonal component” may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat “seasonal component”. Now what you have to do is to augment your data set with 6 dummies representing the days of the week and perhaps monthly indicators to represent annual effects. Now consider incorporating events such as holidays and include any lead, contemoraneous or lag effect around these known variables. No there may be unusual values (pulses) or level shifts or local time trends in the data. Furthermore the day-of-the-week effects may have changed over time e.g. there was no Saturday effect for the first 20 weeks but a Saturday effect for the last 50 weeks.If you wish to post tour daily data I will give it a try and maybe other readers of the list might also contribute their analysis to help guide you through this.
Source : Auto.arima with daily data: how to capture seasonality/periodicity?
4.3.2 Modelling SARIMA
4.3.2.1 Seasonal Data
- Seasonality not taken account of in
auto.arima()compares few models and concludes that the harmonics ARIMA is the best fit model. - Non-stepwise model will slow down the seasonal model.
a$arma[c(1, 6, 2, 3, 7, 4, 5)]is \((p,d,q)(P,D,Q)_{s}\).- How does R’s auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA errors? talk about the OCSB test where Major changes to the forecast package describe the improvement in
forecastpackage. - Frequency parameter and its impact on auto.arima results talk about the frequency parameter for
seasonal periodwhile the author offorecastpackage provides Seasonal periods where describe very details on theseasonal periodparameters determination. - Auto.arima with daily data: how to capture seasonality/periodicity?, the author of
forecastpackage answeredsalests <- ts(data,start=2010,frequency=7)andmodArima <- auto.arima(salests)for weekly seasonality determination. - Why is this xts frequency always 1?
Improved auto.arima() The
auto.arima()function is widely used for automatically selecting ARIMA models. It works quite well, except that selection of \(D\), the order of seasonal differencing, has always been poor. Up until now, the default has been to use the Canova-Hansen test to select \(D\). Because the CH test has a null hypothesis of deterministic seasonality based on dummy variables, the function will often select \(D=0\). So I’ve now switched to using the OCSB test for selecting \(D\) which has a null hypothesis involving a seasonal difference, so it is much more likely to choose \(D=1\) than previously. I’ve done extensive testing of the forecasts obtained under the two methods, and the OCSB test leads to better forecasts. Hence it is now the default. This means that the function may return a different ARIMA model than previously when the data are seasonal. A separate function for selecting the seasonal order has also been made visible. So you can now callnsdiffs()to find the recommended number of seasonal differences without calling auto.arima(). There is also andiffs()function for selecting the number of first differences. Withinauto.arima(),nsdiffs()is called first to select \(D\), and thenndiffs()is applied todiff(x,D)if \(D > 0\) or to \(x\) if \(D=0\).
Double-seasonal Holt-Winters The new dshw() function implements Taylor’s (2003) double-seasonal Holt-Winters method. This allows for two levels of seasonality. For example, with hourly data, there is often a daily period of 24 and a weekly period of 168. These are modelled separately in the
dshw()function.
I am planning some major new functionality to extend this to the various types of complex seasonality discussed in my recent JASA paper. Hopefully that will be ready in the next few weeks – I have a research assistant working on the new code.
Source : Major changes to the forecast package
- Forecasting Daily Data with Multiple Seasonality in R provides the example for seasonal modelling. Now we start modelling harmonics model (which is using
xreg). - R/msts.R introduced a multi seasonal time series objects, intended to be used for models that support multiple seasonal periods. The msts class inherits from the ts class and has an additional “msts” attribute which contains the vector of seasonal periods. All methods that work on a ts class, should also work on a msts class.
- Multiseasonal models for multivariate time series and Forecast double seasonal time series with multiple linear regression in R provides example for multi-seasonal modelling.
- How to setup
xregargument inauto.arima()in R? [closed] usingxregfor multivariate modelling. - Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier introduced 3 seasonal modelling.
- R - Putting time series with frequency of 20 min into the function
stl() - “Frequency” value for seconds/minutes intervals data in R
- Time Series and Forecasting using R
library(forecast)
# create some artifical data
modelfitsample <- data.frame(Customer_Visit=rpois(49,3000),Weekday=rep(1:7,7),
Christmas=c(rep(0,40),1,rep(0,8)),Day=1:49)
# Create matrix of numeric predictors
xreg <- cbind(Weekday=model.matrix(~as.factor(modelfitsample$Weekday)),
Day=modelfitsample$Day,
Christmas=modelfitsample$Christmas)
# Remove intercept
xreg <- xreg[,-1]
# Rename columns
colnames(xreg) <- c("Mon","Tue","Wed","Thu","Fri","Sat","Day","Christmas")
# Variable to be modelled
visits <- ts(modelfitsample$Customer_Visit, frequency=7)
# Find ARIMAX model
modArima <- auto.arima(visits, xreg=xreg)Source : How to setup xreg argument in auto.arima() in R? [closed]
library(forecast)
ts_ <- ts(PaulsData$Temperature, frequency = 1)
msts_ <- msts(ts_, c(7,30,365))
fit <- auto.arima(ts_, seasonal=F, xreg=fourier(msts_, K=c(3,5,10))) # i,j,kts_ <- data_m1$close %>%
ts()
mts_ <- data_m1 %>%
msts(seasonal.periods = c(1440, 7200), start = index(.)[1])
fit1 <- auto.arima(ts_, seasonal = FALSE, xreg=fourier(mts_, K=c(3,5,10)))
fit2 <- auto.arima(ts_, seasonal = FALSE, xreg=mts_)
fit3 <- auto.arima(ts_, D = 1, xreg=mts_)
## https://stackoverflow.com/questions/12161984/how-to-elegantly-convert-datetime-from-decimal-to-d-m-y-hms
## https://stackoverflow.com/questions/17738746/r-putting-time-series-with-frequency-of-20-min-into-the-function-stl
## https://stats.stackexchange.com/questions/120806/frequency-value-for-seconds-minutes-intervals-data-in-r
## http://manishbarnwal.com/blog/2017/05/03/time_series_and_forecasting_using_R/
smp %>%
tk_ts(start = index(index)[1], frequency = c(1440, 7200)) %>%
forecast %>%
llply(tk_tbl)4.3.2.2 Weekly >> Daily ts()
Here I use ts() for seasonal data modeling and set auto.arima(D = 1, seasonal = TRUE) as sarima model, sarimax models will be modeled in next paper.
- Auto.arima with xreg in R, restriction on forecast periods
- How to setup xreg argument in auto.arima() in R?
- Introducing seasonality to an ARIMA model in R
- Seasonality not taken account of in
auto.arima() - purrr auto.arima xreg combination
- Forecasting using R - Dynamic Regression (ch5).pdf
- Daily timeseries forecasting, with weekly and annual cycle
- Forecasting Daily Data with Multiple Seasonality in R
- Time Series Forecasting, a Summarize of Data visualization and prediction
- Time Series Analysis and Forecasting with the TSstudio Package
- Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier
I set the length of dataset as nested seasonal dataset as weekly (1 week = 5 trading days = 7200 minutes) and daily (1 trading day = 1440 minutes).
# --------- eval=FALSE ---------
# sample, not run
> suppressWarnings(Y2015W1 %>%
tk_xts %>%
to.daily %>%
Cl %>%
opt_arma(arma=TRUE))
Using column `index` for date_var.
p d q P D Q s
0 0 0 0 0 0 1# --------- eval=FALSE ---------
# eval(parse(text = paste0(fs, "<- read_rds('", fls[[7]], "') %>% as_tibble")))
# sample, not run
sarima <- list()
for(i in (1:length(fs))) {
smp <- data_m1 %>% tk_xts(silent = TRUE)
timeID <- c(index(smp), xts::last(index(smp)) + minutes(1)) %>%
.[. > force_tz(ymd_hms('2015-01-05 00:00:00 EET'))]
if (dt %in% timeID) {
smp <- smp[paste0(dt, '/', dt %m+% weeks(1) - seconds(59))]
sarima[[i]] <- tryCatch({llply(price_type, function(y) {
df = auto.arima(smp, parallel=FALSE, num.cores = 2)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
}) %>% as_tibble %>% bind_rows}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(sarima[[i]])[3])))
dir.create(paste0('data/fx/', names(sarima[[i]])[3]))
saveRDS(sarima[[i]], paste0(
'data/fx/', names(sarima[[i]])[3], '/sarima.',
unique(sarima[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(sarima[[i]])[3], '/sarima.',
unique(sarima[[i]]$Date), '.rds saved!\n'))
}
}# --------- eval=FALSE ---------
# sample, not run
smp <- data_m1 %>% tk_xts(silent = TRUE)
timeID <- c(index(smp), xts::last(index(smp)) + minutes(1)) %>%
.[. > force_tz(ymd_hms('2015-01-05 00:00:00 EET'))]
dt <- timeID[1]
smp <- smp[paste0(dt, '/', dt %m+% weeks(1) - seconds(59))]
smp %>% tk_ts %>% forecast %>% llply(tk_tbl)
mts <- multi_seasons(smp)
aar <- multi_seasons(smp, auto_arima=TRUE)Below Arima() and auto.arima() functions prove that auto.arima() is better model since it auto adjust the best arima(p,d,q) values.
# --------- eval=FALSE ---------
# sample, not run
> n <- 2000
> m <- 200
> y <- ts(rnorm(n) + (1:n)%%100/30, f=m)
> library(forecast)
> fit <- Arima(y, order=c(2,0,1), xreg=fourier(y, K=4))
> fit
Series: y
Regression with ARIMA(2,0,1) errors
Coefficients:
ar1 ar2 ma1 intercept S1-200 C1-200 S2-200 C2-200 S3-200 C3-200 S4-200
0.3846 0.0649 -0.2794 1.6168 0.0354 0.0308 -1.0026 -0.0222 0.0677 -0.0163 -0.5295
s.e. 0.1588 0.0324 0.1584 0.0320 0.0453 0.0452 0.0452 0.0451 0.0450 0.0450 0.0448
C4-200
0.0059
s.e. 0.0447
sigma^2 estimated as 1.204: log likelihood=-3017.65
AIC=6061.3 AICc=6061.49 BIC=6134.11
> fit2 <- auto.arima(y, seasonal=FALSE, xreg=fourier(y, K=4))
> fit2
Series: y
Regression with ARIMA(1,0,2) errors
Coefficients:
ar1 ma1 ma2 intercept S1-200 C1-200 S2-200 C2-200 S3-200 C3-200 S4-200
0.4605 -0.3566 0.0605 1.6168 0.0354 0.0309 -1.0026 -0.0222 0.0677 -0.0164 -0.5296
s.e. 0.1319 0.1322 0.0297 0.0319 0.0451 0.0451 0.0450 0.0450 0.0449 0.0449 0.0447
C4-200
0.0057
s.e. 0.0447
sigma^2 estimated as 1.204: log likelihood=-3017.44
AIC=6060.87 AICc=6061.06 BIC=6133.69
> fit$aic
[1] 6061.302
> fit2$aic
[1] 6060.873Modeling
# --------- eval=FALSE ---------
# measure as sample take from next chunk
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
dt <- timeID[1]
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sarimats <- smp %>%
tk_ts(frequency = 1440)
##
fit_ts <- auto.arima(Op(sarimats), D = 1)#, trace = TRUE)
saveRDS(fit_ts, 'data/fx/USDJPY/sarima_ts_sample.rds')
##
fr_ts <- forecast(fit_ts, h = 1440)
saveRDS(fr_ts, 'data/fx/USDJPY/sarima_frts_sample.rds')
##
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
fr_ts.sample <- as_tibble(data.frame(index = sq, fr_ts)) %>%
dplyr::select(index, Point.Forecast)
dt.sample <- dplyr::filter(data_m1, index %in% fr_ts.sample$index) %>%
dplyr::select(index, open)
fr_ts.sample <- join(dt.sample, fr_ts.sample) %>%
as_tibble %>%
dplyr::rename(sarima_ts = Point.Forecast)
if(!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(fr_ts.sample, paste0('data/fx/USDJPY/fr_ts.sample.wk.1440.',
as_date(fr_ts.sample$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/fr_ts.sample.wk.1440.',
as_date(fr_ts.sample$index[1]), '.rds saved!\n'))Due to above model consume few hours, here I can only use a sample to compare the accuracy.
# --------- eval=FALSE ---------
#Not run
#sq <- seq(1 , length(data_m1$index), by = 1440)
#sets <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sarimats <- smp %>%
tk_ts(frequency = 1440)
#https://stackoverflow.com/a/37046276/3806250 #auto.arima(x, D = 1)
#https://stackoverflow.com/a/37400899/3806250 #auto.arima(x, seasonal = TRUE)
sarimats <- llply(., function(x) {
auto.arima(x, D = 1) %>% #, trace = TRUE) %>%
forecast(h = 1440)
}) %>%
llply(tk_tbl)
## ----------------------------------------
## Not yet test run
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
dtf <- as_tibble(data.frame(index = sq, sarimats)) %>%
dplyr::select(index, Point.Forecast)
dts <- dplyr::filter(data_m1, index %in% dtf$index) %>%
dplyr::select(index, open)
dtf <- join(dt.sample, dtf) %>%
as_tibble
if(!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(dtf, paste0('data/fx/USDJPY/sarima_ts.wk.1440.',
as_date(dtf$index[1]), '.rds'))
cat(paste0('data/fx/USDJPY/sarima_ts.wk.1440.',
as_date(dtf$index[1]), '.rds saved!\n'))
## ----------------------------------------
}4.3.2.3 Monthly >> Weekly >> Daily ts()
I set the length of dataset as 3 level nested seasonal dataset as monthly (), weekly (1 week = 5 trading days = 7200 minutes) and daily (1 trading day = 1440 minutes).
4.3.2.4 Yearly >> Weekly >> Daily ts()
I set the length of dataset as 3 level nested seasonal dataset as monthly (1 year = ), weekly (1 week = 5 trading days = 7200 minutes) and daily (1 trading day = 1440 minutes).
4.3.2.5 Weekly >> Daily msts()
Modeling
# --------- eval=FALSE ---------
# measure as sample take from next chunk
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
dt <- timeID[1]
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
## Dataset has 7200 observations which is 7200 mins per week
## due to not enough data to run, here I set as 60 mins and 1440 mins, therefore it can loop 5 days.
#mts <- smp %>%
# msts(seasonal.periods = c(1440, 7200))
sarimamsts <- smp %>%
msts(seasonal.periods = c(60, 1440))
##
fit_msts <- auto.arima(Op(sarimamsts), D = 1)#, trace = TRUE)
saveRDS(fit_msts, 'data/fx/USDJPY/sarima_msts_sample.rds')
##
fr_msts <- forecast(fit_msts, h = 1440)
saveRDS(fr_msts, 'data/fx/USDJPY/sarima_frmsts_sample.rds')
##
##
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
fr_msts.sample <- data.frame(index = sq, fr_msts) %>%
dplyr::select(index, Point.Forecast) %>% as_tibble
rownames(fr_msts.sample) <- NULL
dt.sample <- dplyr::filter(data_m1, index %in% fr_msts.sample$index) %>%
dplyr::select(index, open)
fr_msts.sample <- join(dt.sample, fr_msts.sample) %>%
as_tibble %>%
dplyr::rename(sarima_msts = Point.Forecast)
if(!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(fr_msts.sample, paste0('data/fx/USDJPY/fr_msts.sample.wk.1440.',
as_date(fr_msts.sample$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/fr_msts.sample.wk.1440.',
as_date(fr_msts.sample$index[1]), '.rds saved!\n'))# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
sarimamsts <- smp %>%
msts(seasonal.periods = c(1440, 7200))
sarimamsts <- llply(1:ncol(sarimamsts), function(i) {
y <- sarimamsts[,i] %>%
auto.arima(D = 1) %>%
forecast(h = 1440) %>%
as_tibble
#names(y)[1] <- names(smp)[i]
#names(y)[2:ncol(y)] <- paste0(names(y)[1], '.', names(y)[2:ncol(y)])
#names(y)[1] <- paste0(names(smp)[i], '.Point.Forecast')
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
bind_cols %>%
as_tibble
sarimamsts <- sarimamsts[c('open.Point.Forecast', 'high.Point.Forecast', 'low.Point.Forecast', 'close.Point.Forecast',
'open.Lo.80', 'open.Hi.80', 'open.Lo.95', 'open.Hi.95',
'high.Lo.80', 'high.Hi.80', 'high.Lo.95', 'high.Hi.95',
'low.Lo.80', 'low.Hi.80', 'low.Lo.95', 'low.Hi.95',
'close.Lo.80', 'close.Hi.80', 'close.Lo.95', 'close.Hi.95')]
#sarimamsts[str_detect(names(sarimamsts), 'Model.|Period.')] <- NULL
## ----------------------------------------
## Not yet test run if(is.numeric(index(sarimamsts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(sarimamsts) / length(sq)
sarimamsts <- cbind(index = rep(sq, n), sarimamsts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#sarimamsts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sarimamsts, paste0('data/fx/USDJPY/sarimamsts.sample.dy.wk.',
as_date(sarimamsts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sarimamsts.sample.dy.wk.',
as_date(sarimamsts$index[1]), '.rds saved!\n'))
## ----------------------------------------
}Due to above model consume few hours, here I can only use a sample to compare the accuracy.
4.4 TBATS forecast::tbats()
4.4.1 Modelling
- R/msts.R introduced a multi seasonal time series objects, intended to be used for models that support multiple seasonal periods. The msts class inherits from the ts class and has an additional “msts” attribute which contains the vector of seasonal periods. All methods that work on a ts class, should also work on a msts class.
- About
tbatstalk about the modeltbats. - Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier introduced 3 seasonal modelling.
- How to store forecasted values using ‘forecast’ library in R into a CSV file? talk about how to retrieve the forecasted values.
- Forecasting Time Series with Complex Seasonal Patterns using Exponential Smoothing introduce a nested seasonal exponential smoothing model and concludes that trigonometric
tbatsmodel produce lower RMSE and better thanBATSmodel.
4.4.2 Nested Daily-Weekly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
#names(y)[1] <- names(smp)[i]
#names(y)[2:ncol(y)] <- paste0(names(y)[1], '.', names(y)[2:ncol(y)])
#names(y)[1] <- paste0(names(smp)[i], '.Point.Forecast')
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
bind_cols %>%
as_tibble
mts <- mts[c('open.Point.Forecast', 'high.Point.Forecast', 'low.Point.Forecast', 'close.Point.Forecast',
'open.Lo.80', 'open.Hi.80', 'open.Lo.95', 'open.Hi.95',
'high.Lo.80', 'high.Hi.80', 'high.Lo.95', 'high.Hi.95',
'low.Lo.80', 'low.Hi.80', 'low.Lo.95', 'low.Hi.95',
'close.Lo.80', 'close.Hi.80', 'close.Lo.95', 'close.Hi.95')]
#mts[str_detect(names(mts), 'Model.|Period.')] <- NULL
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.wk.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.wk.',
as_date(mts$index[1]), '.rds saved!\n'))
}4.4.3 Nested Daily-Weekly-Monthly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(1) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200, nrow(smp)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.mo'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
join_all %>%
as_tibble
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.wk.mo.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.wk.mo.',
as_date(mts$index[1]), '.rds saved!\n'))
}4.4.4 Nested Daily-Weekly-Quarterly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200, nrow(smp)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.qt'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
join_all %>%
as_tibble
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.wk.qt.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.wk.qt.',
as_date(mts$index[1]), '.rds saved!\n'))
}Due to heavily calculation and based on the comparison section proved that 2 levels (or layers) nested model more effective than 3 levels (or layers) models, here I skip above model.
4.4.5 Nested Daily-Weekly-Yearly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200, nrow(smp)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.yr'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
join_all %>%
as_tibble
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.wk.yr.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.wk.yr.',
as_date(mts$index[1]), '.rds saved!\n'))
}Due to heavily calculation and based on the comparison section proved that 2 levels (or layers) nested model more effective than 3 levels (or layers) models, here I skip above model.
4.4.6 Nested Daily-Weekly-Monthly-Quarterly-Yearly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
##https://robjhyndman.com/hyndsight/seasonal-periods/
yr1 <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
qt1 <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200, nrow(qt1), nrow(yr1)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.qt.yr'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
join_all %>%
as_tibble
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.wk.qt.yr.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.wk.qt.yr.',
as_date(mts$index[1]), '.rds saved!\n'))
}Due to heavily calculation and based on the comparison section proved that 2 levels (or layers) nested model more effective than 3 levels (or layers) models, here I skip above model.
4.4.7 Nested Daily-Quarterly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, nrow(smp)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.qt'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
}) %>%
bind_cols %>%
as_tibble
mts <- mts[c('open.Point.Forecast', 'high.Point.Forecast', 'low.Point.Forecast', 'close.Point.Forecast',
'open.Lo.80', 'open.Hi.80', 'open.Lo.95', 'open.Hi.95',
'high.Lo.80', 'high.Hi.80', 'high.Lo.95', 'high.Hi.95',
'low.Lo.80', 'low.Hi.80', 'low.Lo.95', 'low.Hi.95',
'close.Lo.80', 'close.Hi.80', 'close.Lo.95', 'close.Hi.95')]
#mts[str_detect(names(mts), 'Model.|Period.')] <- NULL
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.qt.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.qt.',
as_date(mts$index[1]), '.rds saved!\n'))
}4.4.8 Nested Daily-Yearly Model
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% years(1) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, nrow(smp)))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>%
bind_rows %>%
mutate(Model = factor('tbats'), Period = factor('dy.yr'), type = case_when(
!is.na(open) ~ 'open',
!is.na(high) ~ 'high',
!is.na(low) ~ 'low',
!is.na(close) ~ 'close')) %>%
dlply(.(type, Period), function(x) {
x %<>% dplyr::rename(open.Point.Forecast = open,
high.Point.Forecast = high,
low.Point.Forecast = low,
close.Point.Forecast = close)
names(x)[str_detect(names(x), '80|95')] <- paste0(x$type[1], '.', names(x)[str_detect(names(x), '80|95')])
x[colSums(!is.na(x)) > 0] %<>%
data.frame %>%
as_tibble %>%
dplyr::select(-type)
#x[c(ncol(x), ncol(x)-1, x[1:(ncol(x)-2)])] #Due to xts format attr, there will be not in order.
}) %>%
bind_cols %>%
as_tibble
mts <- mts[c('open.Point.Forecast', 'high.Point.Forecast', 'low.Point.Forecast', 'close.Point.Forecast',
'open.Lo.80', 'open.Hi.80', 'open.Lo.95', 'open.Hi.95',
'high.Lo.80', 'high.Hi.80', 'high.Lo.95', 'high.Hi.95',
'low.Lo.80', 'low.Hi.80', 'low.Lo.95', 'low.Hi.95',
'close.Lo.80', 'close.Hi.80', 'close.Lo.95', 'close.Hi.95')]
#mts[str_detect(names(mts), 'Model.|Period.')] <- NULL
if(is.numeric(index(mts)[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
n <- nrow(mts) / length(sq)
mts <- cbind(index = rep(sq, n), mts) %>%
as_tibble
} else {
stop('index of dataset does not assign.')
#mts$forecast$index <- data_m1$index[
#(which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1):(
# which(data_m1$index == smp %>%
# index %>%
# xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(mts, paste0('data/fx/USDJPY/mts.dy.yr.',
as_date(mts$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/mts.dy.yr.',
as_date(mts$index[1]), '.rds saved!\n'))
}seasonal_m1 <- read_rds('data/fx/USDJPY/seasonal_m1.rds')
yr_2018 <- data.table(seasonal_m1)[as_date(index) > as_date('2017-12-31')]
dy.qt_dy.yr_2018 <- yr_2018[Model == 'tbats' & Period %in% c('dy.qt', 'dy.yr')]4.4.9 Nested Weekly-Weekly Model
Based on the comparison section proved that daily (1440 mins) nested model more effective than weekly (7200 mins) nested models, here I skip above model.
4.4.10 Nested Weekly-Monthly Model
Based on the comparison section proved that daily (1440 mins) nested model more effective than weekly (7200 mins) nested models, here I skip above model.
4.4.11 Nested Weekly-Quarterly Model
Based on the comparison section proved that daily (1440 mins) nested model more effective than weekly (7200 mins) nested models, here I skip above model.
4.4.12 Nested Weekly-Yearly Model
Based on the comparison section proved that daily (1440 mins) nested model more effective than weekly (7200 mins) nested models, here I skip above model.
## Due to notice there have bias on `qt` and `yr` models after 2 years 2020 from 2018... might probably due to different reasons.
## mts.dy.wk.
ffl <- list.files('data/fx/USDJPY', pattern = 'mts.dy.wk.[0-9]{4}')
smp <- llply(ffl, function(x) {
read_rds(paste0('data/fx/USDJPY/', x))
})
smp_wk <- smp %>%
bind_rows()
smp_wk %<>%
.[c('index', 'open.Point.Forecast', 'high.Point.Forecast',
'low.Point.Forecast', 'close.Point.Forecast')]
smp_wk <- join(data_m1, smp_wk)
smp_wk %<>%
tibble %>%
na.omit
## mts.dy.wk.mo
ffl <- list.files('data/fx/USDJPY', pattern = 'mts.dy.wk.mo.[0-9]{4}')
smp <- llply(ffl, function(x) {
read_rds(paste0('data/fx/USDJPY/', x))
})
smp_wk.mo <- smp %>%
bind_rows()
smp_wk.mo %<>%
.[c('index', 'open.Point.Forecast', 'high.Point.Forecast',
'low.Point.Forecast', 'close.Point.Forecast')]
smp_wk.mo <- join(data_m1, smp_wk.mo)
smp_wk.mo %<>%
tibble %>%
na.omit
## mts.dy.qt.
ffl <- list.files('data/fx/USDJPY', pattern = 'mts.dy.qt.[0-9]{4}')
smp <- llply(ffl, function(x) {
read_rds(paste0('data/fx/USDJPY/', x))
})
smp_qt <- smp %>%
bind_rows()
smp_qt %<>%
.[c('index', 'open.Point.Forecast', 'high.Point.Forecast',
'low.Point.Forecast', 'close.Point.Forecast')]
smp_qt <- join(data_m1, smp_qt)
smp_qt %<>%
tibble %>%
na.omit
## mts.dy.yr.
ffl <- list.files('data/fx/USDJPY', pattern = 'mts.dy.yr.[0-9]{4}')
smp <- llply(ffl, function(x) {
read_rds(paste0('data/fx/USDJPY/', x))
})
smp_yr <- smp %>%
bind_rows()
smp_yr %<>%
.[c('index', 'open.Point.Forecast', 'high.Point.Forecast',
'low.Point.Forecast', 'close.Point.Forecast')]
smp_yr <- join(data_m1, smp_yr)
smp_yr %<>%
tibble %>%
na.omit
rm(ffl, smp)
## trace and check the bias
smp_wkc <- smp_wk %>%
ddply(.(date = as_date(index)), summarise,
MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
n = length(index)) %>%
as_tibble
smp_wkc <- data.frame(model = factor('mts.dy.wk'), smp_wkc) %>%
tibble
smp_wk.moc <- smp_wk.mo %>%
ddply(.(date = as_date(index)), summarise,
MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
n = length(index)) %>%
as_tibble
smp_wk.moc <- data.frame(model = factor('mts.dy.wk.mo'), smp_wk.moc) %>%
tibble
smp_qtc <- smp_qt %>%
ddply(.(date = as_date(index)), summarise,
MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
n = length(index)) %>%
as_tibble
smp_qtc <- data.frame(model = factor('mts.dy.qt'), smp_qtc) %>%
tibble
smp_yrc <- smp_yr %>%
ddply(.(date = as_date(index)), summarise,
MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
n = length(index)) %>%
as_tibble
smp_yrc <- data.frame(model = factor('mts.dy.yr'), smp_yrc) %>%
tibble
smpp <- list(smp_wkc, smp_wk.moc, smp_qtc, smp_yrc) %>%
bind_rows
MSE.open <- smpp %>%
dplyr::select(date, model, MSE.open, n) %>%
spread(model, MSE.open) %>%
na.omit %>%
mutate(mean = rowMeans(
select(., mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr)))
MSE.high <- smpp %>%
dplyr::select(date, model, MSE.high, n) %>%
spread(model, MSE.high) %>%
na.omit %>%
mutate(mean = rowMeans(
select(., mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr)))
MSE.low <- smpp %>%
dplyr::select(date, model, MSE.low, n) %>%
spread(model, MSE.low) %>%
na.omit %>%
mutate(mean = rowMeans(
select(., mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr)))
MSE.close <- smpp %>%
dplyr::select(date, model, MSE.close, n) %>%
spread(model, MSE.close) %>%
na.omit %>%
mutate(mean = rowMeans(
select(., mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr)))
select(MSE.open, c(mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr, mean)) %>% colMeans
# mts.dy.wk mts.dy.wk.mo mts.dy.qt mts.dy.yr mean
# 0.2931847 0.3066926 0.6637179 3.0892483 1.0882109
select(MSE.high, c(mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr, mean)) %>% colMeans
# mts.dy.wk mts.dy.wk.mo mts.dy.qt mts.dy.yr mean
# 0.2824914 0.3044910 0.6679225 3.1030069 1.0894780
select(MSE.low, c(mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr, mean)) %>% colMeans
# mts.dy.wk mts.dy.wk.mo mts.dy.qt mts.dy.yr mean
# 0.2798276 0.3028962 0.6615109 3.0781766 1.0806028
select(MSE.close, c(mts.dy.wk, mts.dy.wk.mo, mts.dy.qt, mts.dy.yr, mean)) %>% colMeans
# mts.dy.wk mts.dy.wk.mo mts.dy.qt mts.dy.yr mean
# 0.2997343 0.2947651 0.6627861 3.0969951 1.0885702> list(smp_wkc, smp_wk.moc, smp_qtc, smp_yrc) %>%
l_ply(function(x) length(x$n), .print = TRUE)
[1] 1084
[1] 1076
[1] 1084
[1] 1084
chk1 <- MSE.open %>%
mutate(
diff1 = abs(mts.dy.wk - mean),
diff2 = abs(mts.dy.wk.mo - mean),
diff3 = abs(mts.dy.qt - mean),
diff4 = abs(mts.dy.yr - mean)) %>%
mutate_if(is.numeric, round, 4) %>%
data.frame
chk1a <- chk1 %>%
dplyr::filter(diff1 >= 0.05 | diff2 >= 0.05 | diff3 >= 0.05 | diff4 >= 0.05)
chk1a[1:100,]4.5 Seasonal Models seasonal::seas()
# --------- eval=FALSE ---------
#sq <- seq(1 , length(data_m1$index), by = 1440)
#mts <- list()
timeID <- data_m1$index %>%
as_date %>%
unique %>%
sort
timeID %<>% .[. > as_date('2015-01-11')]
for (dt in timeID) {
smp <- data_m1 %>%
tk_xts(silent = TRUE)
dt %<>% as_date
smp <- smp[paste0(dt %m-% weeks(1) + seconds(59), '/', dt + seconds(59))]
mts <- smp %>%
msts(seasonal.periods = c(1440, 7200))
mts <- llply(1:ncol(mts), function(i) {
y <- mts[,i] %>%
tbats %>%
forecast(h = 1440) %>%
as_tibble
names(y)[1] <- names(smp)[i]
y
}) %>% bind_rows
if(is.double(mts$forecast$index[1])){
sq <- smp %>%
tail(1) %>%
index
if(weekdays(sq) == '土曜日'|weekdays(sq) == 'Saturday') sq <- sq + days(2)
sq <- seq(from = sq + minutes(1), sq + days(1), by = 'min')
mts$forecast$index <- sq
} else {
mts$forecast$index <- data_m1$index[
(which(data_m1$index == smp %>%
index %>%
xts::last()) + 1):(
which(data_m1$index == smp %>%
index %>%
xts::last()) + 1440)]
}
if (!dir.exists(paste0('data/fx/USDJPY')))
dir.create(paste0('data/fx/USDJPY'))
saveRDS(sets, paste0('data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds'))
cat(paste0(
'data/fx/USDJPY/sets.wk.1440.',
as_date(sets$forecast$index[1]), '.rds saved!\n'))
}4.6 MIDAS
Mixed Frequency Data Sampling Regression Models - The R Package midasr introduce a midas model.
4.7 GARCH-MIDAS
4.8 mcsGARCH
I have just noticed there has another GARCH model in rugarch package and then I roughly read through below articles. This multiplicative component GARCH model is different with normal GARCH model due to it includes the effects of volatility within a day. It is designate for intraday dataset.
- High Frequency GARCH: The multiplicative component GARCH (mcsGARCH) model
- Simulating returns from ARMA(1,1) - mcsGARCH(1,1) model
- Query about mcsGARCH (rugarch package)
- R语言改进高频GARCH模型：乘法分量GARCH（mcsGARCH）模型
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
mcsGARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
mcsGARCH[[i]] <- tryCatch({llply(price_type, function(y) {
df = uv_fx(smp, .model = 'mcsGARCH', currency = cr_code[i],
price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
}) %>% as_tibble %>% bind_rows}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(mcsGARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(mcsGARCH[[i]])[3]))
saveRDS(mcsGARCH[[i]], paste0(
'data/fx/', names(mcsGARCH[[i]])[3], '/mcsGARCH.',
unique(mcsGARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(mcsGARCH[[i]])[3], '/mcsGARCH.',
unique(mcsGARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}4.9 Levy Process
5 Comparison
5.1 1 min per unit
5.1.1 Seasonal ts and msts
Here I read the saved models.
## Get all files.
fls <- paste0('data/fx/USDJPY/', list.files(
'data/fx/USDJPY/', pattern = '^sets|^mts'))
## Shows example.
# read_rds(grep('sets', fls, value = TRUE)[1])
# read_rds(grep('mts', fls, value = TRUE)[1]) %>% as_tibble
seasonal_m <- llply(fls, function(x) {
if(str_detect(x, 'sets.wk.1440.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('wk.1440'))
} else if(str_detect(x, 'sets.mo.1440.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('mo.1440'))
} else if(str_detect(x, 'sets.qt.1440.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('qt.1440'))
} else if(str_detect(x, 'sets.yr.1440.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('yr.1440'))
} else if(str_detect(x, 'sets.wk.7200.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('wk.7200'))
} else if(str_detect(x, 'sets.mo.7200.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('mo.7200'))
} else if(str_detect(x, 'sets.qt.7200.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('qt.7200'))
} else if(str_detect(x, 'sets.yr.7200.')) {
read_rds(x)$forecast %>%
mutate(Model = factor('ts'), Period = factor('yr.7200'))
} else if(str_detect(x, 'mts.dy.wk.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk'))
} else if(str_detect(x, 'mts.dy.qt.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.qt'))
} else if(str_detect(x, 'mts.dy.yr.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.yr'))
} else if(str_detect(x, 'mts.wk.qt.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('wk.qt'))
} else if(str_detect(x, 'mts.wk.qt.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('wk.yr'))
} else if(str_detect(x, 'mts.qt.yr.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('qt.yr'))
} else if(str_detect(x, 'mts.dy.wk.mo.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.mo'))
} else if(str_detect(x, 'mts.dy.wk.mo.qt.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.mo.qt'))
} else if(str_detect(x, 'mts.dy.wk.mo.yr.[0-9]{4}')) {
read_rds(x) %>%
mutate(Model = factor('tbats'), Period = factor('dy.wk.mo.yr'))
} else {
cat('No such files.\n')
}
}) %>%
bind_rows %>%
as_tibble
# seasonal_m[c('Lo.80',
# 'close.Lo.80', 'close.Hi.80', 'close.Lo.95', 'close.Hi.95',
# 'high.Hi.80', 'high.Lo.95', 'high.Hi.95',
# 'high.high.Point.Forecast', 'low.Hi.80', 'low.Lo.95',
# 'low.Hi.95', 'open.Hi.80', 'open.Lo.95', 'open.Hi.95',
# 'open.Lo.80', 'high.Lo.80', 'low.Lo.80', 'close.Lo.80')] <- NULL
## don't use complete.cases() since there has some NA elements in ts models.
#seasonal_m <- seasonal_m[complete.cases(seasonal_m),]
#dataset with 23
write_rds(seasonal_m, 'data/fx/USDJPY/seasonal_m.rds')
seasonal_m1 <- seasonal_m
rm(seasonal_m, data_m1)
seasonal_m1 %<>%
.[c('index','Model','Period',
'open.Point.Forecast','high.Point.Forecast',
'low.Point.Forecast','close.Point.Forecast')]#,
# 'open.Point.Forecast.Hi 80','open.Point.Forecast.Lo 80',
# 'open.Point.Forecast.Lo 95','open.Point.Forecast.Hi 95',
# 'high.Point.Forecast.Lo 80','high.Point.Forecast.Hi 80',
# 'high.Point.Forecast.Lo 95','high.Point.Forecast.Hi 95',
# 'low.Point.Forecast.Lo 80','low.Point.Forecast.Hi 80',
# 'low.Point.Forecast.Lo 95','low.Point.Forecast.Hi 95',
# 'close.Point.Forecast.Lo 80','close.Point.Forecast.Hi 80',
# 'close.Point.Forecast.Lo 95','close.Point.Forecast.Hi 95')]
##
#seasonal_m <- llply(fls, function(x) {
# read_rds(x)$forecast %>%
# mutate(
# Model = case_when(
# grepl('sets.wk.1440.', x) ~ factor('ts'),
# grepl('sets.mo.1440.', x) ~ factor('ts'),
# grepl('sets.qt.1440.', x) ~ factor('ts'),
# grepl('sets.yr.1440.', x) ~ factor('ts'),
# grepl('sets.wk.7200.', x) ~ factor('ts'),
# grepl('sets.mo.7200.', x) ~ factor('ts'),
# grepl('sets.qt.7200.', x) ~ factor('ts'),
# grepl('sets.yr.7200.', x) ~ factor('ts'),
# grepl('mts.dy.wk.[0-9]{4}', x) ~ factor('tbats'),
# grepl('mts.dy.wk.mo.[0-9]{4}', x) ~ factor('tbats'),
# grepl('mts.dy.wk.mo.qt.[0-9]{4}', x) ~ factor('tbats'),
# grepl('mts.dy.wk.mo.yr.[0-9]{4}', x) ~ factor('tbats'),
# FALSE~ stop('No such files.')),
# Period = factor('wk.1440'),
# Period = factor('mo.1440'),
# Period = factor('qt.1440'),
# Period = factor('yr.1440'),
# Period = factor('wk.7200'),
# Period = factor('mo.7200'),
# Period = factor('qt.7200'),
# Period = factor('yr.7200'),
# Period = factor('dy.wk'),
# Period = factor('dy.wk.mo'),
# Period = factor('dy.wk.mo.qt'),
# Period = factor('dy.wk.mo.yr'))
#
#} else {
# stop('No such files.')
#}
# }) %>%
# bind_rows %>%
# as_tibble
##The last observation of Friday is Saturday 00:00:00 but not next Monday 00:00:00. Therefore the Saturday forecasted price will not be merge with Next Monday market price.
#comp %<>% .[colSums(!is.na(.)) > 0]
seasonal_m1 <- join(data_m1, seasonal_m1) %>%
bind_rows %>%
as_tibble
seasonal_m1 %<>%
.[c('index','Model','Period','open','high','low','close',
'open.Point.Forecast','high.Point.Forecast',
'low.Point.Forecast','close.Point.Forecast')]#,
# 'open.Point.Forecast.Hi 80','open.Point.Forecast.Lo 80',
# 'open.Point.Forecast.Lo 95','open.Point.Forecast.Hi 95',
# 'high.Point.Forecast.Lo 80','high.Point.Forecast.Hi 80',
# 'high.Point.Forecast.Lo 95','high.Point.Forecast.Hi 95',
# 'low.Point.Forecast.Lo 80','low.Point.Forecast.Hi 80',
# 'low.Point.Forecast.Lo 95','low.Point.Forecast.Hi 95',
# 'close.Point.Forecast.Lo 80','close.Point.Forecast.Hi 80',
# 'close.Point.Forecast.Lo 95','close.Point.Forecast.Hi 95')]
seasonal_m1 %<>% na.omit
## don't use complete.cases() since there has some NA elements in ts models.
#seasonal_m <- seasonal_m[complete.cases(seasonal_m),]
write_rds(seasonal_m1, 'data/fx/USDJPY/seasonal_m1.rds')
#zip it to be splited 99MB for each file.
## ------------------------------------------
## zip above files to be splitted small files since file sizes restriction on GitHub.
## ------------------------------------------#dir('data/fx/USDJPY', pattern = '*.z') %>%
# llply(., function(x) {
# suppressAll(unzip(paste0('data/fx/USDJPY/', x)))
# })
seasonal_m1 <- read_rds('data/fx/USDJPY/seasonal_m1.rds')
## https://stackoverflow.com/a/52490634/3806250
#seasonal_m1[is.nan(seasonal_m1)] <- NA5.1.1.1 Line Graph & Trend
Below graph shows the forecast price and actual price.
5.1.1.1.1 Overview
grph <- seasonal_m1 %>%
tidyr::unite(Model, Model:Period) %>%
data.table
prc <- unique(grph[, .(index, open, high, low, close)])
prc <- prc[, Model := 'Market.Price'][]
grph <- grph[, (c('open', 'high', 'low', 'close')) := NULL]
names(grph) <- c('index', 'Model', 'open', 'high', 'low', 'close')
grph <- rbind(grph, prc)
grph <- data.table(grph)[order(index)]
rm(prc)
## save dataset in data.table format
saveRDS(grph, 'data/fx/USDJPY/grph.rds')
# fwrite(data.table(grph), 'data/fx/USDJPY/grph.csv')
# write.table(data.table(grph), 'data/fx/USDJPY/grph.txt')
## https://rstudio-pubs-static.s3.amazonaws.com/31702_9c22e3d1a0c44968a4a1f9656f1800ab.html
grph_json <- rjson::toJSON(grph)
write(grph_json, 'data/fx/USDJPY/grph_json.json')
#grph_json <- fromJSON('data/fx/USDJPY/grph_json.json')grph <- readRDS('data/fx/USDJPY/grph.rds')
data.frame(grph)[c(1:5, (nrow(grph)-5):nrow(grph)),] %>%
kbl('html', caption = 'Data Sample', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '100%')| index | Model | open | high | low | close | |
|---|---|---|---|---|---|---|
| 1 | 2015-01-12 00:01:00 | tbats_dy.qt | 118.5390 | 118.5614 | 118.5230 | 118.5480 |
| 2 | 2015-01-12 00:01:00 | tbats_dy.wk | 118.5390 | 118.5614 | 118.5230 | 118.5480 |
| 3 | 2015-01-12 00:01:00 | tbats_dy.yr | 118.5390 | 118.5614 | 118.5230 | 118.5480 |
| 4 | 2015-01-12 00:01:00 | ts_mo.1440 | 118.5907 | 118.6257 | 118.5749 | 118.6095 |
| 5 | 2015-01-12 00:01:00 | ts_mo.7200 | 118.5390 | 118.5626 | 118.5260 | 118.5480 |
| 18849595 | 2018-07-07 00:00:00 | ts_wk.7200 | 110.6450 | 110.6435 | 110.5675 | 110.5737 |
| 18849596 | 2018-07-07 00:00:00 | ts_wk.7200 | 110.6450 | 110.6435 | 110.5675 | 110.5737 |
| 18849597 | 2018-07-07 00:00:00 | ts_wk.7200 | 110.6450 | 110.6435 | 110.5675 | 110.5737 |
| 18849598 | 2018-07-07 00:00:00 | ts_wk.7200 | 110.6450 | 110.6435 | 110.5675 | 110.5737 |
| 18849599 | 2018-07-07 00:00:00 | ts_yr.1440 | 110.6449 | 110.6492 | 110.5636 | 110.5707 |
| 18849600 | 2018-07-07 00:00:00 | Market.Price | 110.4635 | 110.4540 | 110.4770 | 110.4740 |
the dataset above has 18849600 x, 6 x dimensions.
## https://plotly.com/r/embedding-graphs-in-rmarkdown
## https://stackoverflow.com/questions/25186022/embedding-plotly-output-in-r-markdown/25192691
##
fig <- plot_ly(grph, x = ~index, y = ~open, color = ~Model)
fig <- fig %>% add_lines()
fig5.1.1.1.2 Open Price
## ------------ eval = FALSE -------------------
## Due to high volume dataset and heavily ploting, here I ommit it.
grph %>%
group_by(Model) %>%
e_charts(x = index) %>%
e_line(open.Point.Forecast, smooth = TRUE) %>%
e_datazoom(
type = 'slider',
toolbox = FALSE,
bottom = -5) %>%
e_tooltip() %>%
e_title(text = 'Model', subtext = 'open.Point.Forecast', left = 'center') %>%
e_axis_labels(x = 'index', y = 'open.Point.Forecast') %>%
e_x_axis(index, axisPointer = list(show = TRUE)) %>%
e_legend(
orient = 'vertical',
type = c('scroll'),
#selectedMode = 'multiple', #https://echarts.apache.org/en/option.html#legend
#selected = list('Model'),
left = 0, top = 80) %>%
e_grid(left = 150, top = 90) %>%
#e_theme('shine') %>%
e_toolbox_feature('saveAsImage', title = 'Screenshot')## ggthemes
palettes1 <- ggthemes_data[['tableau']][['color-palettes']][['ordered-sequential']]
## https://github.com/BTJ01/ggthemes/blob/master/inst/examples/ex-scale_color_tableau.R
palettes2 <- ggthemes_data[["tableau"]][["color-palettes"]][["regular"]]
## -------------------------------
## ggthemr
## https://www.shanelynn.ie/themes-and-colours-for-r-ggplots-with-ggthemr/
#tableau_colours <- c('#1F77B4', '#FF7F0E', '#2CA02C', '#D62728', '#9467BD', '#8C564B', '#CFECF9', '#7F7F7F', '#BCBD22', '#17BECF')
tableau_colours <- palettes2$`Tableau 20`$value
names(tableau_colours) <- palettes2$`Tableau 20`$name
#names(tableau_colours) <- unique(grph$Model)
## https://colorbrewer2.org/#type=qualitative&scheme=Paired&n=12
#tableau_colours <- c('#a6cee3', '#1f78b4', '#b2df8a', '#33a02c', '#fb9a99', '#e31a1c', '#fdbf6f', '#ff7f00', '#cab2d6', '#6a3d9a', '#ffff99', '#b15928')
# you have to add a colour at the start of your palette for outlining boxes, we'll use a grey:
#tableau_colours <- c("#555555", tableau_colours)
# remove previous effects:
ggthemr_reset()
# Define colours for your figures with define_palette
tableau <- define_palette(
swatch = tableau_colours, # colours for plotting points and bars
## https://stackoverflow.com/questions/7014387/whats-the-difference-between-1l-and-1
gradient = c(lower = tableau_colours[1L], upper = tableau_colours[length(tableau_colours)]), #upper and lower colours for continuous colours
#background = "#EEEEEE" #defining a grey-ish background
)
# set the theme for your figures:
ggthemr(tableau)
## ------------------------
## https://stackoverflow.com/questions/34601194/change-colours-to-defined-palette-for-ggplot-objects
change_colours <- function(p, palette) {
n <- nlevels(p$data[[deparse(p$mapping$group)]])
tryCatch(as.character(palette),
error=function(e) stop('palette should be a vector of colours', call.=FALSE))
if(n > length(palette)) stop('Not enough colours in palette.')
pal <- function(n) palette[seq_len(n)]
p + theme_light() + discrete_scale('colour', 'foo', pal)
}## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p1 <- grph %>%
ggplot(aes(x = index, y = open, group = Model, color = Model)) +
geom_line() +
#scale_colour_gradient2_tableau(palette = names(palettes)[1]) + #first palettes list in name
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Open Price Forecasting',
subtitle = paste('From', range(unique(grph$index))[1L], 'to', range(unique(grph$index))[2L]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
##scale_fill_manual(values = tableau_colours) +
#scale_color_brewer(tableau_colours) +
#scale_color_jcolors(palette = palettes2$`Tableau 20`$value) + #choose color set among palettes
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
#ggplotly(p1)
p1
5.1.1.1.3 High Price
rm(p1)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p2 <- grph %>%
ggplot(aes(x = index, y = high, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min High Price Forecasting',
subtitle = paste('From', range(unique(grph$index))[1L], 'to', range(unique(grph$index))[2L]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
#ggplotly(p2)
p2
5.1.1.1.4 Low Price
rm(p2)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p3 <- grph %>%
ggplot(aes(x = index, y = low, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Low Price Forecasting',
subtitle = paste('From', range(unique(grph$index))[1], 'to', range(unique(grph$index))[2]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
#ggplotly(p3)
p3
5.1.1.1.5 Close Price
rm(p3)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p4 <- grph %>%
ggplot(aes(x = index, y = close, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Close Price Forecasting',
subtitle = paste('From', range(unique(grph$index))[1], 'to', range(unique(grph$index))[2]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
#ggplotly(p4)
p4
5.1.1.2 MSE Table
Below table compares the models.
rm(p4)
mse1 <- seasonal_m1 %>%
ddply(.(Model, Period), summarise,
MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
n = length(index)) %>%
as_tibbletb6 <- mse1 %>%
mutate(
MSE.open = ifelse(
rank(MSE.open) <= 3,
cell_spec(
paste0(round(MSE.open, 7), ' (rank: ', sprintf('%1.f', rank(MSE.open)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.open, 7), ' (rank: ', sprintf('%1.f', rank(MSE.open)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.high = ifelse(
rank(MSE.high) <= 3,
cell_spec(
paste0(round(MSE.high, 7), ' (rank: ', sprintf('%1.f', rank(MSE.high)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.high, 7), ' (rank: ', sprintf('%1.f', rank(MSE.high)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.low = ifelse(
rank(MSE.low) <= 3,
cell_spec(
paste0(round(MSE.low, 7), ' (rank: ', sprintf('%1.f', rank(MSE.low)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.low, 7), ' (rank: ', sprintf('%1.f', rank(MSE.low)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.close = ifelse(
rank(MSE.close) <= 3,
cell_spec(
paste0(round(MSE.close, 7), ' (rank: ', sprintf('%1.f', rank(MSE.close)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.close, 7), ' (rank: ', sprintf('%1.f', rank(MSE.close)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.HLC = ifelse(
rank(MSE.HLC) <= 3,
cell_spec(
paste0(round(MSE.HLC, 7), ' (rank: ', sprintf('%1.f', rank(MSE.HLC)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.HLC, 7), ' (rank: ', sprintf('%1.f', rank(MSE.HLC)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.OHLC = ifelse(
rank(MSE.OHLC) <= 3,
cell_spec(
paste0(round(MSE.OHLC, 7), ' (rank: ', sprintf('%1.f', rank(MSE.OHLC)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.OHLC, 7), ' (rank: ', sprintf('%1.f', rank(MSE.OHLC)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'MSE of Seasonal Daily 1440 minutes ETS Model (Accumulated Period from Weekly)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
column_spec(7, background = 'Gainsboro') %>%
column_spec(8, background = 'LightGray') %>%
column_spec(9, background = 'LightSlateGrey') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
rm(mse1)
tb6| Model | Period | MSE.open | MSE.high | MSE.low | MSE.close | MSE.HLC | MSE.OHLC | n |
|---|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 0.5935084 (rank: 11) | 0.5946396 (rank: 11) | 0.593577 (rank: 11) | 0.59344 (rank: 11) | 0.5938855 (rank: 11) | 0.5937912 (rank: 11) | 1298880 |
| tbats | dy.wk | 0.2331241 (rank: 1) | 0.2305384 (rank: 1) | 0.2331357 (rank: 1) | 0.2415673 (rank: 4) | 0.2350805 (rank: 2) | 0.2345914 (rank: 1) | 1298880 |
| tbats | dy.wk.mo | 0.2585134 (rank: 6) | 0.2531527 (rank: 7) | 0.2511519 (rank: 6) | 0.2468493 (rank: 5) | 0.2503846 (rank: 6) | 0.2524168 (rank: 6) | 1287360 |
| tbats | dy.yr | 2.992332 (rank: 12) | 3.0002451 (rank: 12) | 2.989127 (rank: 12) | 3.0017416 (rank: 12) | 2.9970379 (rank: 12) | 2.9958614 (rank: 12) | 1298880 |
| ts | mo.1440 | 0.238598 (rank: 4) | 0.2372364 (rank: 4) | 0.2349181 (rank: 4) | 0.2378324 (rank: 3) | 0.2366623 (rank: 4) | 0.2371462 (rank: 4) | 1298880 |
| ts | mo.7200 | 0.3134664 (rank: 8) | 0.3146787 (rank: 8) | 0.3119626 (rank: 8) | 0.3142609 (rank: 7) | 0.3136341 (rank: 8) | 0.3135922 (rank: 8) | 244800 |
| ts | qt.1440 | 0.2355912 (rank: 2) | 0.2357561 (rank: 2) | 0.2346795 (rank: 2) | 0.234693 (rank: 1) | 0.2350429 (rank: 1) | 0.2351799 (rank: 2) | 1298880 |
| ts | qt.7200 | 0.3156878 (rank: 9) | 0.3167276 (rank: 9) | 0.3144045 (rank: 9) | 0.3168899 (rank: 8) | 0.3160073 (rank: 9) | 0.3159275 (rank: 9) | 223200 |
| ts | wk.1440 | 0.2525562 (rank: 5) | 0.2483678 (rank: 6) | 0.2491352 (rank: 5) | 0.2490372 (rank: 6) | 0.2488467 (rank: 5) | 0.2497741 (rank: 5) | 1298880 |
| ts | wk.7200 | 0.2850686 (rank: 7) | 0.2391797 (rank: 5) | 0.3065442 (rank: 7) | 0.32009 (rank: 9) | 0.2886046 (rank: 7) | 0.2877206 (rank: 7) | 6494400 |
| ts | yr.1440 | 0.2357672 (rank: 3) | 0.2359108 (rank: 3) | 0.2349109 (rank: 3) | 0.2348683 (rank: 2) | 0.23523 (rank: 3) | 0.2353643 (rank: 3) | 1298880 |
| ts | yr.7200 | 0.3342637 (rank: 10) | 0.3353777 (rank: 10) | 0.3327021 (rank: 10) | 0.335306 (rank: 10) | 0.3344619 (rank: 10) | 0.3344124 (rank: 10) | 208800 |
from above models we know the βest model.
5.1.2 Interday Models
Here I summarize 1440 of 1 min data to be 1 day and choose the best fitted model. Below table compares the models.
# mse2 <- seasonal_m1 %>%
# ddply(.(Model, Period, index), summarise,
# MSE.open = mean((open.Point.Forecast - open)^2, na.rm=TRUE),
# MSE.high = mean((high.Point.Forecast - high)^2, na.rm=TRUE),
# MSE.low = mean((low.Point.Forecast - low)^2, na.rm=TRUE),
# MSE.close = mean((close.Point.Forecast - close)^2, na.rm=TRUE),
# MSE.HLC = (MSE.high + MSE.low + MSE.close)/3,
# MSE.OHLC = (MSE.open + MSE.high + MSE.low + MSE.close)/4,
# n = length(index)) %>%
# as_tibble
## https://tysonbarrett.com/jekyll/update/2019/10/06/datatable_memory/
## http://brooksandrew.github.io/simpleblog/articles/advanced-data-table/
seasonal_m1 <- data.table(seasonal_m1)
setorder(seasonal_m1, index)
open.accr <- seasonal_m1[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
high.accr <- seasonal_m1[, {
high = high
high.Point.Forecast = high.Point.Forecast
.SD[, .(.N, high.mape = MAPE(high, high.Point.Forecast),
high.smape = SMAPE(high, high.Point.Forecast),
high.mse = MSE(high, high.Point.Forecast),
high.rmse = RMSE(high, high.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
low.accr <- seasonal_m1[, {
low = low
low.Point.Forecast = low.Point.Forecast
.SD[, .(.N, low.mape = MAPE(low, low.Point.Forecast),
low.smape = SMAPE(low, low.Point.Forecast),
low.mse = MSE(low, low.Point.Forecast),
low.rmse = RMSE(low, low.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
close.accr <- seasonal_m1[, {
close = close
close.Point.Forecast = close.Point.Forecast
.SD[, .(.N, close.mape = MAPE(close, close.Point.Forecast),
close.smape = SMAPE(close, close.Point.Forecast),
close.mse = MSE(close, close.Point.Forecast),
close.rmse = RMSE(close, close.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]open.sm <- open.accr[, list(open.mape = mean(open.mape),
open.smape = mean(open.smape),
open.mse = mean(open.mse),
open.rmse = mean(open.rmse)),
by=.(Model, Period)]
high.sm <- high.accr[, list(high.mape = mean(high.mape),
high.smape = mean(high.smape),
high.mse = mean(high.mse),
high.rmse = mean(high.rmse)),
by=.(Model, Period)]
low.sm <- low.accr[, list(low.mape = mean(low.mape),
low.smape = mean(low.smape),
low.mse = mean(low.mse),
low.rmse = mean(low.rmse)),
by=.(Model, Period)]
close.sm <- close.accr[, list(close.mape = mean(close.mape),
close.smape = mean(close.smape),
close.mse = mean(close.mse),
close.rmse = mean(close.rmse)),
by=.(Model, Period)]
daily.sm <- join_all(list(open.sm, high.sm, low.sm, close.sm)) %>%
tibble
saveRDS(daily.sm, 'data/fx/USDJPY/best_m.rds')5.1.2.1 Open Price
daily.sm <- readRDS('data/fx/USDJPY/best_m.rds')
tb7 <- daily.sm %>%
dplyr::select(contains(c('Model', 'Period', 'open'))) %>%
mutate(
open.mape = ifelse(
rank(open.mape) <= 3,
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.smape = ifelse(
rank(open.smape) <= 3,
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.mse = ifelse(
rank(open.mse) <= 3,
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
open.rmse = ifelse(
rank(open.rmse) <= 3,
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min Open Price Summarised to 1 Day per Unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb7| Model | Period | open.mape | open.smape | open.mse | open.rmse |
|---|---|---|---|---|---|
| tbats | dy.qt | 0.0038487 (rank: 8) | 0.0038663 (rank: 8) | 0.6615488 (rank: 11) | 0.4836051 (rank: 8) |
| tbats | dy.wk | 0.0031178 (rank: 2) | 0.0031203 (rank: 2) | 0.2951857 (rank: 4) | 0.4022059 (rank: 1) |
| tbats | dy.yr | 0.0078141 (rank: 12) | 0.007929 (rank: 12) | 3.0602275 (rank: 12) | 0.9279223 (rank: 12) |
| ts | mo.1440 | 0.0031302 (rank: 4) | 0.0031321 (rank: 4) | 0.2895257 (rank: 3) | 0.4044655 (rank: 4) |
| ts | mo.7200 | 0.0041186 (rank: 10) | 0.0041147 (rank: 10) | 0.425753 (rank: 9) | 0.5564735 (rank: 10) |
| ts | qt.1440 | 0.0031176 (rank: 1) | 0.0031195 (rank: 1) | 0.2870498 (rank: 1) | 0.4030116 (rank: 2) |
| ts | qt.7200 | 0.004058 (rank: 9) | 0.0040546 (rank: 9) | 0.42255 (rank: 8) | 0.5479559 (rank: 9) |
| ts | wk.1440 | 0.0032485 (rank: 7) | 0.0032503 (rank: 7) | 0.3038581 (rank: 5) | 0.4183746 (rank: 7) |
| ts | wk.7200 | 0.0031907 (rank: 6) | 0.0031914 (rank: 6) | 0.3388586 (rank: 7) | 0.412083 (rank: 6) |
| ts | yr.1440 | 0.0031196 (rank: 3) | 0.0031215 (rank: 3) | 0.2872197 (rank: 2) | 0.4032139 (rank: 3) |
| ts | yr.7200 | 0.0042881 (rank: 11) | 0.0042843 (rank: 11) | 0.4553046 (rank: 10) | 0.5785254 (rank: 11) |
| tbats | dy.wk.mo | 0.0031517 (rank: 5) | 0.003155 (rank: 5) | 0.3068028 (rank: 6) | 0.4058541 (rank: 5) |
5.1.2.2 High Price
tb8 <- daily.sm %>%
dplyr::select(contains(c('Model', 'Period', 'high'))) %>%
mutate(
high.mape = ifelse(
rank(high.mape) <= 3,
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.smape = ifelse(
rank(high.smape) <= 3,
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mse = ifelse(
rank(high.mse) <= 3,
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.rmse = ifelse(
rank(high.rmse) <= 3,
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min High Price Summarised to 1 Day per Unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb8| Model | Period | high.mape | high.smape | high.mse | high.rmse |
|---|---|---|---|---|---|
| tbats | dy.qt | 0.0038673 (rank: 8) | 0.0038852 (rank: 8) | 0.6658388 (rank: 11) | 0.4855776 (rank: 8) |
| tbats | dy.wk | 0.0030783 (rank: 1) | 0.0030807 (rank: 1) | 0.2846739 (rank: 1) | 0.397453 (rank: 1) |
| tbats | dy.yr | 0.0078297 (rank: 12) | 0.0079453 (rank: 12) | 3.0739678 (rank: 12) | 0.9298084 (rank: 12) |
| ts | mo.1440 | 0.0031371 (rank: 5) | 0.0031392 (rank: 5) | 0.2918493 (rank: 4) | 0.4052568 (rank: 5) |
| ts | mo.7200 | 0.0041905 (rank: 10) | 0.0041868 (rank: 10) | 0.4366597 (rank: 9) | 0.5650381 (rank: 10) |
| ts | qt.1440 | 0.0031227 (rank: 3) | 0.0031248 (rank: 3) | 0.288908 (rank: 2) | 0.4035778 (rank: 3) |
| ts | qt.7200 | 0.004129 (rank: 9) | 0.0041259 (rank: 9) | 0.4333607 (rank: 8) | 0.5565739 (rank: 9) |
| ts | wk.1440 | 0.0032312 (rank: 7) | 0.0032334 (rank: 7) | 0.3002029 (rank: 6) | 0.4159632 (rank: 7) |
| ts | wk.7200 | 0.0031119 (rank: 2) | 0.0031138 (rank: 2) | 0.2986969 (rank: 5) | 0.401548 (rank: 2) |
| ts | yr.1440 | 0.0031252 (rank: 4) | 0.0031273 (rank: 4) | 0.2890714 (rank: 3) | 0.4038346 (rank: 4) |
| ts | yr.7200 | 0.0043671 (rank: 11) | 0.0043636 (rank: 11) | 0.467057 (rank: 10) | 0.5881937 (rank: 11) |
| tbats | dy.wk.mo | 0.0031592 (rank: 6) | 0.0031622 (rank: 6) | 0.3054827 (rank: 7) | 0.4065748 (rank: 6) |
5.1.2.3 Low Price
tb9 <- daily.sm %>%
dplyr::select(contains(c('Model', 'Period', 'low'))) %>%
mutate(
low.mape = ifelse(
rank(low.mape) <= 3,
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.smape = ifelse(
rank(low.smape) <= 3,
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mse = ifelse(
rank(low.mse) <= 3,
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.rmse = ifelse(
rank(low.rmse) <= 3,
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min Open Price Summarised to 1 Day per Unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb9| Model | Period | low.mape | low.smape | low.mse | low.rmse |
|---|---|---|---|---|---|
| tbats | dy.qt | 0.0038604 (rank: 8) | 0.0038777 (rank: 8) | 0.6593377 (rank: 11) | 0.4847373 (rank: 8) |
| tbats | dy.wk | 0.0030658 (rank: 1) | 0.0030678 (rank: 1) | 0.2820305 (rank: 1) | 0.3962719 (rank: 1) |
| tbats | dy.yr | 0.0078086 (rank: 12) | 0.0079229 (rank: 12) | 3.0492512 (rank: 12) | 0.9272861 (rank: 12) |
| ts | mo.1440 | 0.0031155 (rank: 3) | 0.0031171 (rank: 3) | 0.2833452 (rank: 4) | 0.4027251 (rank: 3) |
| ts | mo.7200 | 0.0040769 (rank: 10) | 0.0040725 (rank: 10) | 0.4221267 (rank: 9) | 0.5517966 (rank: 10) |
| ts | qt.1440 | 0.0031147 (rank: 2) | 0.0031162 (rank: 2) | 0.2829726 (rank: 2) | 0.4026439 (rank: 2) |
| ts | qt.7200 | 0.0039968 (rank: 9) | 0.0039929 (rank: 9) | 0.4190357 (rank: 8) | 0.5412921 (rank: 9) |
| ts | wk.1440 | 0.0032298 (rank: 6) | 0.0032312 (rank: 6) | 0.2968221 (rank: 5) | 0.4159053 (rank: 6) |
| ts | wk.7200 | 0.0032465 (rank: 7) | 0.0032471 (rank: 7) | 0.3657361 (rank: 7) | 0.4186519 (rank: 7) |
| ts | yr.1440 | 0.0031173 (rank: 4) | 0.0031188 (rank: 4) | 0.2831797 (rank: 3) | 0.4029436 (rank: 4) |
| ts | yr.7200 | 0.0042393 (rank: 11) | 0.004235 (rank: 11) | 0.4522995 (rank: 10) | 0.5732734 (rank: 11) |
| tbats | dy.wk.mo | 0.0031814 (rank: 5) | 0.0031842 (rank: 5) | 0.3030913 (rank: 6) | 0.4089394 (rank: 5) |
5.1.2.4 Close Price
tb10 <- daily.sm %>%
dplyr::select(contains(c('Model', 'Period', 'close'))) %>%
mutate(
close.mape = ifelse(
rank(close.mape) <= 3,
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.smape = ifelse(
rank(close.smape) <= 3,
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mse = ifelse(
rank(close.mse) <= 3,
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.rmse = ifelse(
rank(close.rmse) <= 3,
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min Close Price Summarised to 1 Day per Unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb10| Model | Period | close.mape | close.smape | close.mse | close.rmse |
|---|---|---|---|---|---|
| tbats | dy.qt | 0.0038503 (rank: 8) | 0.0038679 (rank: 8) | 0.6610232 (rank: 11) | 0.4837561 (rank: 8) |
| tbats | dy.wk | 0.003145 (rank: 5) | 0.0031473 (rank: 5) | 0.3015154 (rank: 6) | 0.4057309 (rank: 5) |
| tbats | dy.yr | 0.0078135 (rank: 12) | 0.0079289 (rank: 12) | 3.0682874 (rank: 12) | 0.9280099 (rank: 12) |
| ts | mo.1440 | 0.0031304 (rank: 4) | 0.003132 (rank: 4) | 0.2874381 (rank: 3) | 0.4044561 (rank: 4) |
| ts | mo.7200 | 0.0041607 (rank: 10) | 0.0041564 (rank: 10) | 0.4379246 (rank: 9) | 0.5616704 (rank: 10) |
| ts | qt.1440 | 0.0031164 (rank: 1) | 0.0031182 (rank: 1) | 0.284739 (rank: 1) | 0.4028578 (rank: 2) |
| ts | qt.7200 | 0.0040893 (rank: 9) | 0.0040855 (rank: 9) | 0.4356525 (rank: 8) | 0.5524039 (rank: 9) |
| ts | wk.1440 | 0.0032319 (rank: 7) | 0.0032337 (rank: 7) | 0.2995034 (rank: 5) | 0.4162795 (rank: 7) |
| ts | wk.7200 | 0.0031979 (rank: 6) | 0.0031966 (rank: 6) | 0.3632592 (rank: 7) | 0.4118763 (rank: 6) |
| ts | yr.1440 | 0.0031187 (rank: 2) | 0.0031205 (rank: 2) | 0.2849251 (rank: 2) | 0.403099 (rank: 3) |
| ts | yr.7200 | 0.0043391 (rank: 11) | 0.0043348 (rank: 11) | 0.4701278 (rank: 10) | 0.5850767 (rank: 11) |
| tbats | dy.wk.mo | 0.0031204 (rank: 3) | 0.0031234 (rank: 3) | 0.2948921 (rank: 4) | 0.4018679 (rank: 1) |
5.1.2.5 Summary
tb11 <- daily.sm %>%
mutate(
open.mape = ifelse(
rank(open.mape) <= 3,
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.smape = ifelse(
rank(open.smape) <= 3,
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.mse = ifelse(
rank(open.mse) <= 3,
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
open.rmse = ifelse(
rank(open.rmse) <= 3,
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mape = ifelse(
rank(high.mape) <= 3,
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.smape = ifelse(
rank(high.smape) <= 3,
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mse = ifelse(
rank(high.mse) <= 3,
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.rmse = ifelse(
rank(high.rmse) <= 3,
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mape = ifelse(
rank(low.mape) <= 3,
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.smape = ifelse(
rank(low.smape) <= 3,
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mse = ifelse(
rank(low.mse) <= 3,
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.rmse = ifelse(
rank(low.rmse) <= 3,
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mape = ifelse(
rank(close.mape) <= 3,
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.smape = ifelse(
rank(close.smape) <= 3,
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mse = ifelse(
rank(close.mse) <= 3,
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.rmse = ifelse(
rank(close.rmse) <= 3,
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min summarised to 1 day per unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
#column_spec(3, background = 'LightSlateGrey') %>%
column_spec(3, background = 'LightGray') %>%
column_spec(4, background = 'Gainsboro') %>%
column_spec(5, background = 'LightGray') %>%
column_spec(6, background = 'Gainsboro') %>%
column_spec(7, background = 'LightGray') %>%
column_spec(8, background = 'Gainsboro') %>%
column_spec(9, background = 'LightGray') %>%
column_spec(10, background = 'Gainsboro') %>%
column_spec(11, background = 'LightGray') %>%
column_spec(12, background = 'Gainsboro') %>%
column_spec(13, background = 'LightGray') %>%
column_spec(14, background = 'Gainsboro') %>%
column_spec(15, background = 'LightGray') %>%
column_spec(16, background = 'Gainsboro') %>%
column_spec(17, background = 'LightGray') %>%
column_spec(18, background = 'Gainsboro') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb11| Model | Period | open.mape | open.smape | open.mse | open.rmse | high.mape | high.smape | high.mse | high.rmse | low.mape | low.smape | low.mse | low.rmse | close.mape | close.smape | close.mse | close.rmse |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 0.0038487 (rank: 8) | 0.0038663 (rank: 8) | 0.6615488 (rank: 11) | 0.4836051 (rank: 8) | 0.0038673 (rank: 8) | 0.0038852 (rank: 8) | 0.6658388 (rank: 11) | 0.4855776 (rank: 8) | 0.0038604 (rank: 8) | 0.0038777 (rank: 8) | 0.6593377 (rank: 11) | 0.4847373 (rank: 8) | 0.0038503 (rank: 8) | 0.0038679 (rank: 8) | 0.6610232 (rank: 11) | 0.4837561 (rank: 8) |
| tbats | dy.wk | 0.0031178 (rank: 2) | 0.0031203 (rank: 2) | 0.2951857 (rank: 4) | 0.4022059 (rank: 1) | 0.0030783 (rank: 1) | 0.0030807 (rank: 1) | 0.2846739 (rank: 1) | 0.397453 (rank: 1) | 0.0030658 (rank: 1) | 0.0030678 (rank: 1) | 0.2820305 (rank: 1) | 0.3962719 (rank: 1) | 0.003145 (rank: 5) | 0.0031473 (rank: 5) | 0.3015154 (rank: 6) | 0.4057309 (rank: 5) |
| tbats | dy.yr | 0.0078141 (rank: 12) | 0.007929 (rank: 12) | 3.0602275 (rank: 12) | 0.9279223 (rank: 12) | 0.0078297 (rank: 12) | 0.0079453 (rank: 12) | 3.0739678 (rank: 12) | 0.9298084 (rank: 12) | 0.0078086 (rank: 12) | 0.0079229 (rank: 12) | 3.0492512 (rank: 12) | 0.9272861 (rank: 12) | 0.0078135 (rank: 12) | 0.0079289 (rank: 12) | 3.0682874 (rank: 12) | 0.9280099 (rank: 12) |
| ts | mo.1440 | 0.0031302 (rank: 4) | 0.0031321 (rank: 4) | 0.2895257 (rank: 3) | 0.4044655 (rank: 4) | 0.0031371 (rank: 5) | 0.0031392 (rank: 5) | 0.2918493 (rank: 4) | 0.4052568 (rank: 5) | 0.0031155 (rank: 3) | 0.0031171 (rank: 3) | 0.2833452 (rank: 4) | 0.4027251 (rank: 3) | 0.0031304 (rank: 4) | 0.003132 (rank: 4) | 0.2874381 (rank: 3) | 0.4044561 (rank: 4) |
| ts | mo.7200 | 0.0041186 (rank: 10) | 0.0041147 (rank: 10) | 0.425753 (rank: 9) | 0.5564735 (rank: 10) | 0.0041905 (rank: 10) | 0.0041868 (rank: 10) | 0.4366597 (rank: 9) | 0.5650381 (rank: 10) | 0.0040769 (rank: 10) | 0.0040725 (rank: 10) | 0.4221267 (rank: 9) | 0.5517966 (rank: 10) | 0.0041607 (rank: 10) | 0.0041564 (rank: 10) | 0.4379246 (rank: 9) | 0.5616704 (rank: 10) |
| ts | qt.1440 | 0.0031176 (rank: 1) | 0.0031195 (rank: 1) | 0.2870498 (rank: 1) | 0.4030116 (rank: 2) | 0.0031227 (rank: 3) | 0.0031248 (rank: 3) | 0.288908 (rank: 2) | 0.4035778 (rank: 3) | 0.0031147 (rank: 2) | 0.0031162 (rank: 2) | 0.2829726 (rank: 2) | 0.4026439 (rank: 2) | 0.0031164 (rank: 1) | 0.0031182 (rank: 1) | 0.284739 (rank: 1) | 0.4028578 (rank: 2) |
| ts | qt.7200 | 0.004058 (rank: 9) | 0.0040546 (rank: 9) | 0.42255 (rank: 8) | 0.5479559 (rank: 9) | 0.004129 (rank: 9) | 0.0041259 (rank: 9) | 0.4333607 (rank: 8) | 0.5565739 (rank: 9) | 0.0039968 (rank: 9) | 0.0039929 (rank: 9) | 0.4190357 (rank: 8) | 0.5412921 (rank: 9) | 0.0040893 (rank: 9) | 0.0040855 (rank: 9) | 0.4356525 (rank: 8) | 0.5524039 (rank: 9) |
| ts | wk.1440 | 0.0032485 (rank: 7) | 0.0032503 (rank: 7) | 0.3038581 (rank: 5) | 0.4183746 (rank: 7) | 0.0032312 (rank: 7) | 0.0032334 (rank: 7) | 0.3002029 (rank: 6) | 0.4159632 (rank: 7) | 0.0032298 (rank: 6) | 0.0032312 (rank: 6) | 0.2968221 (rank: 5) | 0.4159053 (rank: 6) | 0.0032319 (rank: 7) | 0.0032337 (rank: 7) | 0.2995034 (rank: 5) | 0.4162795 (rank: 7) |
| ts | wk.7200 | 0.0031907 (rank: 6) | 0.0031914 (rank: 6) | 0.3388586 (rank: 7) | 0.412083 (rank: 6) | 0.0031119 (rank: 2) | 0.0031138 (rank: 2) | 0.2986969 (rank: 5) | 0.401548 (rank: 2) | 0.0032465 (rank: 7) | 0.0032471 (rank: 7) | 0.3657361 (rank: 7) | 0.4186519 (rank: 7) | 0.0031979 (rank: 6) | 0.0031966 (rank: 6) | 0.3632592 (rank: 7) | 0.4118763 (rank: 6) |
| ts | yr.1440 | 0.0031196 (rank: 3) | 0.0031215 (rank: 3) | 0.2872197 (rank: 2) | 0.4032139 (rank: 3) | 0.0031252 (rank: 4) | 0.0031273 (rank: 4) | 0.2890714 (rank: 3) | 0.4038346 (rank: 4) | 0.0031173 (rank: 4) | 0.0031188 (rank: 4) | 0.2831797 (rank: 3) | 0.4029436 (rank: 4) | 0.0031187 (rank: 2) | 0.0031205 (rank: 2) | 0.2849251 (rank: 2) | 0.403099 (rank: 3) |
| ts | yr.7200 | 0.0042881 (rank: 11) | 0.0042843 (rank: 11) | 0.4553046 (rank: 10) | 0.5785254 (rank: 11) | 0.0043671 (rank: 11) | 0.0043636 (rank: 11) | 0.467057 (rank: 10) | 0.5881937 (rank: 11) | 0.0042393 (rank: 11) | 0.004235 (rank: 11) | 0.4522995 (rank: 10) | 0.5732734 (rank: 11) | 0.0043391 (rank: 11) | 0.0043348 (rank: 11) | 0.4701278 (rank: 10) | 0.5850767 (rank: 11) |
| tbats | dy.wk.mo | 0.0031517 (rank: 5) | 0.003155 (rank: 5) | 0.3068028 (rank: 6) | 0.4058541 (rank: 5) | 0.0031592 (rank: 6) | 0.0031622 (rank: 6) | 0.3054827 (rank: 7) | 0.4065748 (rank: 6) | 0.0031814 (rank: 5) | 0.0031842 (rank: 5) | 0.3030913 (rank: 6) | 0.4089394 (rank: 5) | 0.0031204 (rank: 3) | 0.0031234 (rank: 3) | 0.2948921 (rank: 4) | 0.4018679 (rank: 1) |
Above table summarized the daily mape, smape, mse and rmse values and then summarized again the models (which is nested summarize due to daily settlement), we can interpret from above table :
- Weekly or
7200 minslength’s dataset withmsts(seasonal.periods = c(1440, 7200)) %>% tbats %>% forecast(h = 1440). - Quarterly length’s dataset with
tk_ts(frequency = 1440) %>% forecast(h=1440). - Annum length’s dataset with
tk_ts(frequency = 1440) %>% forecast(h=1440).
5.1.3 Miscellaneous
5.1.3.1 Best Model
#best_model <- seasonal_m1 %>%
# ddply(.(Model, Period), summarize,
# mape = MAPE(open, open.Point.Forecast),
# smape = SMAPE(open, open.Point.Forecast),
# mse = MSE(open, open.Point.Forecast),
# rmse = RMSE(open, open.Point.Forecast))
## https://tysonbarrett.com/jekyll/update/2019/10/06/datatable_memory/
## http://brooksandrew.github.io/simpleblog/articles/advanced-data-table/
if(!is.data.table(seasonal_m1)) seasonal_m1 <- data.table(seasonal_m1)
setorder(seasonal_m1, index)
m.op <- seasonal_m1[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.hi <- seasonal_m1[, {
high = high
high.Point.Forecast = high.Point.Forecast
.SD[, .(.N, high.mape = MAPE(high, high.Point.Forecast),
high.smape = SMAPE(high, high.Point.Forecast),
high.mse = MSE(high, high.Point.Forecast),
high.rmse = RMSE(high, high.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.lo <- seasonal_m1[, {
low = low
low.Point.Forecast = low.Point.Forecast
.SD[, .(.N, low.mape = MAPE(low, low.Point.Forecast),
low.smape = SMAPE(low, low.Point.Forecast),
low.mse = MSE(low, low.Point.Forecast),
low.rmse = RMSE(low, low.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.cl <- seasonal_m1[, {
close = close
close.Point.Forecast = close.Point.Forecast
.SD[, .(.N, close.mape = MAPE(close, close.Point.Forecast),
close.smape = SMAPE(close, close.Point.Forecast),
close.mse = MSE(close, close.Point.Forecast),
close.rmse = RMSE(close, close.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
best_model <- join_all(list(m.op, m.hi, m.lo, m.cl)) %>% tibble
saveRDS(best_model, 'data/fx/USDJPY/best_m_daily.rds')
rm(m.op, m.hi, m.lo, m.cl)best_model <- readRDS('data/fx/USDJPY/best_m_daily.rds')
tb12 <- best_model %>%
mutate(
open.mape = ifelse(
rank(open.mape) <= 3,
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.smape = ifelse(
rank(open.smape) <= 3,
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.mse = ifelse(
rank(open.mse) <= 3,
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
open.rmse = ifelse(
rank(open.rmse) <= 3,
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mape = ifelse(
rank(high.mape) <= 3,
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.smape = ifelse(
rank(high.smape) <= 3,
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mse = ifelse(
rank(high.mse) <= 3,
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.rmse = ifelse(
rank(high.rmse) <= 3,
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mape = ifelse(
rank(low.mape) <= 3,
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.smape = ifelse(
rank(low.smape) <= 3,
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mse = ifelse(
rank(low.mse) <= 3,
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.rmse = ifelse(
rank(low.rmse) <= 3,
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mape = ifelse(
rank(close.mape) <= 3,
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.smape = ifelse(
rank(close.smape) <= 3,
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mse = ifelse(
rank(close.mse) <= 3,
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.rmse = ifelse(
rank(close.rmse) <= 3,
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'LightSlateGrey') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
column_spec(7, background = 'Gainsboro') %>%
column_spec(8, background = 'LightGray') %>%
column_spec(9, background = 'Gainsboro') %>%
column_spec(10, background = 'LightGray') %>%
column_spec(11, background = 'Gainsboro') %>%
column_spec(12, background = 'LightGray') %>%
column_spec(13, background = 'Gainsboro') %>%
column_spec(14, background = 'LightGray') %>%
column_spec(15, background = 'Gainsboro') %>%
column_spec(16, background = 'LightGray') %>%
column_spec(17, background = 'Gainsboro') %>%
column_spec(18, background = 'LightGray') %>%
column_spec(19, background = 'Gainsboro') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb12| Model | Period | N | open.mape | open.smape | open.mse | open.rmse | high.mape | high.smape | high.mse | high.rmse | low.mape | low.smape | low.mse | low.rmse | close.mape | close.smape | close.mse | close.rmse |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 1298880 | 0.0035608 (rank: 10) | 0.0035773 (rank: 10) | 0.5935084 (rank: 11) | 0.770395 (rank: 11) | 0.0035672 (rank: 10) | 0.0035837 (rank: 10) | 0.5946396 (rank: 11) | 0.7711288 (rank: 11) | 0.0035692 (rank: 10) | 0.0035856 (rank: 10) | 0.593577 (rank: 11) | 0.7704395 (rank: 11) | 0.0035606 (rank: 10) | 0.0035771 (rank: 10) | 0.59344 (rank: 11) | 0.7703506 (rank: 11) |
| tbats | dy.wk | 1298880 | 0.002821 (rank: 1) | 0.0028228 (rank: 1) | 0.2331241 (rank: 1) | 0.4828292 (rank: 1) | 0.0027999 (rank: 1) | 0.0028016 (rank: 1) | 0.2305384 (rank: 1) | 0.4801442 (rank: 1) | 0.0028014 (rank: 1) | 0.0028031 (rank: 1) | 0.2331357 (rank: 1) | 0.4828412 (rank: 1) | 0.002839 (rank: 1) | 0.002841 (rank: 1) | 0.2415673 (rank: 4) | 0.4914949 (rank: 4) |
| tbats | dy.wk.mo | 1287360 | 0.0028932 (rank: 5) | 0.0028962 (rank: 5) | 0.2585134 (rank: 6) | 0.5084421 (rank: 6) | 0.002889 (rank: 6) | 0.0028914 (rank: 6) | 0.2531527 (rank: 7) | 0.5031428 (rank: 7) | 0.0029032 (rank: 5) | 0.0029056 (rank: 5) | 0.2511519 (rank: 6) | 0.5011506 (rank: 6) | 0.0028635 (rank: 4) | 0.0028661 (rank: 4) | 0.2468493 (rank: 5) | 0.4968393 (rank: 5) |
| tbats | dy.yr | 1298880 | 0.0075387 (rank: 12) | 0.0076525 (rank: 12) | 2.992332 (rank: 12) | 1.7298358 (rank: 12) | 0.0075476 (rank: 12) | 0.0076617 (rank: 12) | 3.0002451 (rank: 12) | 1.7321216 (rank: 12) | 0.0075415 (rank: 12) | 0.0076552 (rank: 12) | 2.989127 (rank: 12) | 1.7289092 (rank: 12) | 0.0075423 (rank: 12) | 0.0076565 (rank: 12) | 3.0017416 (rank: 12) | 1.7325535 (rank: 12) |
| ts | mo.1440 | 1298880 | 0.002871 (rank: 4) | 0.0028723 (rank: 4) | 0.238598 (rank: 4) | 0.4884649 (rank: 4) | 0.0028638 (rank: 5) | 0.0028652 (rank: 5) | 0.2372364 (rank: 4) | 0.4870692 (rank: 4) | 0.0028605 (rank: 3) | 0.0028618 (rank: 3) | 0.2349181 (rank: 4) | 0.4846835 (rank: 4) | 0.0028733 (rank: 5) | 0.0028745 (rank: 5) | 0.2378324 (rank: 3) | 0.4876807 (rank: 3) |
| ts | mo.7200 | 244800 | 0.0034764 (rank: 8) | 0.0034756 (rank: 8) | 0.3134664 (rank: 8) | 0.5598807 (rank: 8) | 0.0035018 (rank: 8) | 0.0035011 (rank: 8) | 0.3146787 (rank: 8) | 0.5609623 (rank: 8) | 0.0034669 (rank: 8) | 0.0034659 (rank: 8) | 0.3119626 (rank: 8) | 0.5585361 (rank: 8) | 0.0034906 (rank: 8) | 0.0034897 (rank: 8) | 0.3142609 (rank: 7) | 0.5605898 (rank: 7) |
| ts | qt.1440 | 1298880 | 0.0028558 (rank: 2) | 0.0028571 (rank: 2) | 0.2355912 (rank: 2) | 0.4853773 (rank: 2) | 0.0028566 (rank: 3) | 0.002858 (rank: 3) | 0.2357561 (rank: 2) | 0.4855472 (rank: 2) | 0.0028598 (rank: 2) | 0.0028611 (rank: 2) | 0.2346795 (rank: 2) | 0.4844374 (rank: 2) | 0.0028572 (rank: 2) | 0.0028585 (rank: 2) | 0.234693 (rank: 1) | 0.4844512 (rank: 1) |
| ts | qt.7200 | 223200 | 0.0034844 (rank: 9) | 0.0034841 (rank: 9) | 0.3156878 (rank: 9) | 0.561861 (rank: 9) | 0.0035078 (rank: 9) | 0.0035075 (rank: 9) | 0.3167276 (rank: 9) | 0.5627856 (rank: 9) | 0.0034754 (rank: 9) | 0.003475 (rank: 9) | 0.3144045 (rank: 9) | 0.5607179 (rank: 9) | 0.0034988 (rank: 9) | 0.0034984 (rank: 9) | 0.3168899 (rank: 8) | 0.5629298 (rank: 8) |
| ts | wk.1440 | 1298880 | 0.0029887 (rank: 7) | 0.0029899 (rank: 7) | 0.2525562 (rank: 5) | 0.5025497 (rank: 5) | 0.0029757 (rank: 7) | 0.0029772 (rank: 7) | 0.2483678 (rank: 6) | 0.4983651 (rank: 6) | 0.0029796 (rank: 7) | 0.0029807 (rank: 7) | 0.2491352 (rank: 5) | 0.4991344 (rank: 5) | 0.0029779 (rank: 7) | 0.0029791 (rank: 7) | 0.2490372 (rank: 6) | 0.4990362 (rank: 6) |
| ts | wk.7200 | 6494400 | 0.0029027 (rank: 6) | 0.002903 (rank: 6) | 0.2850686 (rank: 7) | 0.5339181 (rank: 7) | 0.0028179 (rank: 2) | 0.0028195 (rank: 2) | 0.2391797 (rank: 5) | 0.48906 (rank: 5) | 0.00295 (rank: 6) | 0.0029496 (rank: 6) | 0.3065442 (rank: 7) | 0.5536644 (rank: 7) | 0.0029287 (rank: 6) | 0.0029266 (rank: 6) | 0.32009 (rank: 9) | 0.565765 (rank: 9) |
| ts | yr.1440 | 1298880 | 0.0028579 (rank: 3) | 0.0028593 (rank: 3) | 0.2357672 (rank: 3) | 0.4855587 (rank: 3) | 0.0028589 (rank: 4) | 0.0028603 (rank: 4) | 0.2359108 (rank: 3) | 0.4857065 (rank: 3) | 0.0028625 (rank: 4) | 0.0028637 (rank: 4) | 0.2349109 (rank: 3) | 0.484676 (rank: 3) | 0.0028594 (rank: 3) | 0.0028607 (rank: 3) | 0.2348683 (rank: 2) | 0.4846321 (rank: 2) |
| ts | yr.7200 | 208800 | 0.0036239 (rank: 11) | 0.0036236 (rank: 11) | 0.3342637 (rank: 10) | 0.5781554 (rank: 10) | 0.0036485 (rank: 11) | 0.0036482 (rank: 11) | 0.3353777 (rank: 10) | 0.5791181 (rank: 10) | 0.0036111 (rank: 11) | 0.0036106 (rank: 11) | 0.3327021 (rank: 10) | 0.5768033 (rank: 10) | 0.0036356 (rank: 11) | 0.0036352 (rank: 11) | 0.335306 (rank: 10) | 0.5790561 (rank: 10) |
Above table summarized the total observations with mape, smape, mse and rmse values (which is not nested summarize not daily settlement for P&L), we can interpret from above table :
- Weekly or
7200 minslength’s dataset withmsts(seasonal.periods = c(1440, 7200)) %>% tbats %>% forecast(h = 1440). - Quarterly length’s dataset with
tk_ts(frequency = 1440) %>% forecast(h=1440). - Annum length’s dataset with
tk_ts(frequency = 1440) %>% forecast(h=1440).
5.1.3.2 Sarima
##Below model use open price dataset where contain 7200 mins and forecast 1440 mins.
fit_ts <- readRDS('data/fx/USDJPY/sarima_ts_sample.rds')
#fr_ts <- forecast(fit_ts, h = 1440)
fr_ts <- readRDS('data/fx/USDJPY/sarima_frts_sample.rds')
fr_ts.sample <- readRDS('data/fx/USDJPY/fr_ts.sample.wk.1440.2015-01-12.rds')
##Below model use open price dataset where contain 7200 mins and forecast nested 60mins & 1440 mins.
fit_msts <- readRDS('data/fx/USDJPY/sarima_msts_sample.rds')
fr_msts <- readRDS('data/fx/USDJPY/sarima_frmsts_sample.rds')
fr_msts.sample <- readRDS('data/fx/USDJPY/fr_msts.sample.wk.1440.2015-01-12.rds')Due to heavily calculation on sarima models, here I only use 1st week from 2015-01-12 00:01:00 to from 2015-01-13 00:00:00` calculate.
cmp1 <- join(fr_ts.sample, fr_msts.sample) %>%
as_tibble
lst1 <- list.files('data/fx/USDJPY', pattern = '^mts.*.2015-01-12.rds$')
cmp2 <- llply(lst1, function(x) {
readRDS(paste0('data/fx/USDJPY/', x)) %>%
dplyr::select(contains(c('index', 'open.Point.Forecast'))) %>% .[,1:2]
})
names(cmp2) <- str_replace_all(lst1, '.[1-9].*', '')
cmp2 %<>% ldply %>%
as_tibble %>%
spread(.id, open.Point.Forecast)
cmp2 <- data.frame(open = cmp1$open, cmp2) %>%
as_tibble %>%
.[c(2:1, 3:ncol(.))]
lst2 <- list.files('data/fx/USDJPY', pattern = '^sets.*.2015-01-12.rds$')
cmp3 <- llply(lst2, function(x) {
readRDS(paste0('data/fx/USDJPY/', x))$forecast %>%
dplyr::select(contains(c('index', 'open.Point.Forecast'))) %>% .[1:1440,1:2]
})
names(cmp3) <- substr(lst2, 1, 12) #manual filter characters
cmp3 %<>% ldply %>%
as_tibble %>%
spread(.id, open.Point.Forecast)
cmp3 <- data.frame(open = cmp1$open, cmp3) %>%
as_tibble %>%
.[c(2:1, 3:ncol(.))]
## ------------------------
cmp1 <- data.frame(
Model = c('sarima_ts', 'sarima_msts'),
n = nrow(cmp1),
mape = c(MAPE(cmp1$open, cmp1$sarima_ts),
MAPE(cmp1$open, cmp1$sarima_msts)),
smape = c(SMAPE(cmp1$open, cmp1$sarima_ts),
SMAPE(cmp1$open, cmp1$sarima_msts)),
mse = c(MSE(cmp1$open, cmp1$sarima_ts),
MSE(cmp1$open, cmp1$sarima_msts)),
rmse = c(RMSE(cmp1$open, cmp1$sarima_ts),
RMSE(cmp1$open, cmp1$sarima_msts))) %>%
tibble
cmp2 <- data.frame(
Model = names(cmp2)[3:ncol(cmp2)],
n = nrow(cmp2),
mape = c(MAPE(cmp2$open, cmp2$mts.dy.qt),
MAPE(cmp2$open, cmp2$mts.dy.wk),
MAPE(cmp2$open, cmp2$mts.dy.wk.mo),
MAPE(cmp2$open, cmp2$mts.dy.yr)),
smape = c(SMAPE(cmp2$open, cmp2$mts.dy.qt),
SMAPE(cmp2$open, cmp2$mts.dy.wk),
SMAPE(cmp2$open, cmp2$mts.dy.wk.mo),
SMAPE(cmp2$open, cmp2$mts.dy.yr)),
mse = c(MSE(cmp2$open, cmp2$mts.dy.qt),
MSE(cmp2$open, cmp2$mts.dy.wk),
MSE(cmp2$open, cmp2$mts.dy.wk.mo),
MSE(cmp2$open, cmp2$mts.dy.yr)),
rmse = c(RMSE(cmp2$open, cmp2$mts.dy.qt),
RMSE(cmp2$open, cmp2$mts.dy.wk),
RMSE(cmp2$open, cmp2$mts.dy.wk.mo),
RMSE(cmp2$open, cmp2$mts.dy.yr))) %>%
tibble
cmp3 <- data.frame(
Model = names(cmp3)[3:ncol(cmp3)],
n = nrow(cmp3),
mape = c(MAPE(cmp3$open, cmp3$sets.mo.1440),
MAPE(cmp3$open, cmp3$sets.mo.7200),
MAPE(cmp3$open, cmp3$sets.qt.1440),
MAPE(cmp3$open, cmp3$sets.qt.7200),
MAPE(cmp3$open, cmp3$sets.wk.1440),
MAPE(cmp3$open, cmp3$sets.wk.7200),
MAPE(cmp3$open, cmp3$sets.yr.1440),
MAPE(cmp3$open, cmp3$sets.yr.7200)),
smape = c(SMAPE(cmp3$open, cmp3$sets.mo.1440),
SMAPE(cmp3$open, cmp3$sets.mo.7200),
SMAPE(cmp3$open, cmp3$sets.qt.1440),
SMAPE(cmp3$open, cmp3$sets.qt.7200),
SMAPE(cmp3$open, cmp3$sets.wk.1440),
SMAPE(cmp3$open, cmp3$sets.wk.7200),
SMAPE(cmp3$open, cmp3$sets.yr.1440),
SMAPE(cmp3$open, cmp3$sets.yr.7200)),
mse = c(MSE(cmp3$open, cmp3$sets.mo.1440),
MSE(cmp3$open, cmp3$sets.mo.7200),
MSE(cmp3$open, cmp3$sets.qt.1440),
MSE(cmp3$open, cmp3$sets.qt.7200),
MSE(cmp3$open, cmp3$sets.wk.1440),
MSE(cmp3$open, cmp3$sets.wk.7200),
MSE(cmp3$open, cmp3$sets.yr.1440),
MSE(cmp3$open, cmp3$sets.yr.7200)),
rmse = c(RMSE(cmp3$open, cmp3$sets.mo.1440),
RMSE(cmp3$open, cmp3$sets.mo.7200),
RMSE(cmp3$open, cmp3$sets.qt.1440),
RMSE(cmp3$open, cmp3$sets.qt.7200),
RMSE(cmp3$open, cmp3$sets.wk.1440),
RMSE(cmp3$open, cmp3$sets.wk.7200),
RMSE(cmp3$open, cmp3$sets.yr.1440),
RMSE(cmp3$open, cmp3$sets.yr.7200))) %>%
tibble
cmp <- bind_rows(cmp1, cmp2, cmp3) %>%
as_tibbletb13 <- cmp %>%
mutate(
mape = ifelse(
rank(mape) <= 3,
cell_spec(
paste0(round(mape, 7), ' (rank: ', sprintf('%1.f', rank(mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(mape, 7), ' (rank: ', sprintf('%1.f', rank(mape)), ')'),
'html', color = 'grey', italic = TRUE)),
smape = ifelse(
rank(smape) <= 3,
cell_spec(
paste0(round(smape, 7), ' (rank: ', sprintf('%1.f', rank(smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(smape, 7), ' (rank: ', sprintf('%1.f', rank(smape)), ')'),
'html', color = 'grey', italic = TRUE)),
mse = ifelse(
rank(mse) <= 3,
cell_spec(
paste0(round(mse, 7), ' (rank: ', sprintf('%1.f', rank(mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(mse, 7), ' (rank: ', sprintf('%1.f', rank(mse)), ')'),
'html', color = 'grey', italic = TRUE)),
rmse = ifelse(
rank(rmse) <= 3,
cell_spec(
paste0(round(rmse, 7), ' (rank: ', sprintf('%1.f', rank(rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(rmse, 7), ' (rank: ', sprintf('%1.f', rank(rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Sarima_ts & Sarima_msts Models etc', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'Gainsboro') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb13| Model | n | mape | smape | mse | rmse |
|---|---|---|---|---|---|
| sarima_ts | 1440 | 0.0046041 (rank: 12) | 0.0045896 (rank: 12) | 0.4452853 (rank: 12) | 0.667297 (rank: 12) |
| sarima_msts | 1440 | 0.0046041 (rank: 12) | 0.0045896 (rank: 12) | 0.4452853 (rank: 12) | 0.667297 (rank: 12) |
| mts.dy.qt | 1440 | 0.0024737 (rank: 6) | 0.0024726 (rank: 6) | 0.1155722 (rank: 6) | 0.3399591 (rank: 6) |
| mts.dy.wk | 1440 | 0.0024737 (rank: 6) | 0.0024726 (rank: 6) | 0.1155722 (rank: 6) | 0.3399591 (rank: 6) |
| mts.dy.wk.mo | 1440 | NA (rank: 14) | NA (rank: 14) | NA (rank: 14) | NA (rank: 14) |
| mts.dy.yr | 1440 | 0.0024737 (rank: 6) | 0.0024726 (rank: 6) | 0.1155722 (rank: 6) | 0.3399591 (rank: 6) |
| sets.mo.1440 | 1440 | 0.0026197 (rank: 10) | 0.0026221 (rank: 10) | 0.1198407 (rank: 10) | 0.3461801 (rank: 10) |
| sets.mo.7200 | 1440 | 0.0024737 (rank: 2) | 0.0024726 (rank: 2) | 0.1155722 (rank: 2) | 0.3399591 (rank: 2) |
| sets.qt.1440 | 1440 | 0.0026197 (rank: 10) | 0.0026221 (rank: 10) | 0.1198407 (rank: 10) | 0.3461801 (rank: 10) |
| sets.qt.7200 | 1440 | 0.0024737 (rank: 2) | 0.0024726 (rank: 2) | 0.1155722 (rank: 2) | 0.3399591 (rank: 2) |
| sets.wk.1440 | 1440 | 0.0026197 (rank: 10) | 0.0026221 (rank: 10) | 0.1198407 (rank: 10) | 0.3461801 (rank: 10) |
| sets.wk.7200 | 1440 | 0.0024737 (rank: 2) | 0.0024726 (rank: 2) | 0.1155722 (rank: 2) | 0.3399591 (rank: 2) |
| sets.yr.1440 | 1440 | 0.0026197 (rank: 10) | 0.0026221 (rank: 10) | 0.1198407 (rank: 10) | 0.3461801 (rank: 10) |
| sets.yr.7200 | 1440 | 0.0024737 (rank: 2) | 0.0024726 (rank: 2) | 0.1155722 (rank: 2) | 0.3399591 (rank: 2) |
Application of auto.arima() on both ts() and msts() seasonal datasets compare the ts() and msts() sarima models.
5.2 1 day per unit
5.2.1 Interday ETS Model
Below I recall the ETS models for interday price prediction in previous paper for comparison.
ets.fls <- list.files('data', pattern = '^[A-Z]{3}\\.[A-Za-z]{4}')
ETS.MSE <- llply(ets.fls, function(x) {
nm <- x %>%
str_replace_all('.rds', '') %>%
str_split_fixed('\\.', 2) %>%
as_data_frame
names(nm) <- c('Model', 'Type')
y <- paste0('data/', x) %>%
read_rds
data.frame(nm, y) %>% as_tibble
}) %>% bind_rows %>%
dplyr::select(Date, Model,Type, Point.Forecast, forClose,
USDJPY.Open, USDJPY.High, USDJPY.Low, USDJPY.Close)
ETS.MSE %<>% mutate(
MSE.1 = case_when(
substr(Type, 1, 2) == 'Op' ~ mean((Point.Forecast - USDJPY.Open)^2,
na.rm = TRUE),
substr(Type, 1, 2) == 'Hi' ~ mean((Point.Forecast - USDJPY.High)^2,
na.rm = TRUE),
substr(Type, 1, 2) == 'Mn' ~ mean((Point.Forecast - (USDJPY.High + USDJPY.Low)/2)^2, na.rm = TRUE),
substr(Type, 1, 2) == 'Lo' ~ mean((Point.Forecast - USDJPY.Low)^2,
na.rm = TRUE),
substr(Type, 1, 2) == 'Cl' ~ mean((Point.Forecast - USDJPY.Close)^2,
na.rm = TRUE)),
MSE.2 = case_when(
substr(Type, 3, 4) == 'Op' ~ mean((Point.Forecast - USDJPY.Open)^2,
na.rm = TRUE),
substr(Type, 3, 4) == 'Hi' ~ mean((Point.Forecast - USDJPY.High)^2,
na.rm = TRUE),
substr(Type, 3, 4) == 'Mn' ~ mean((Point.Forecast - (USDJPY.High + USDJPY.Low)/2)^2, na.rm = TRUE),
substr(Type, 3, 4) == 'Lo' ~ mean((Point.Forecast - USDJPY.Low)^2,
na.rm = TRUE),
substr(Type, 3, 4) == 'Cl' ~ mean((Point.Forecast - USDJPY.Close)^2,
na.rm = TRUE)))
ETS.MSE %<>%
ddply(.(Model, Type), summarise,
MSE.1 = mean(MSE.1, na.rm=TRUE),
MSE.2 = mean(MSE.2, na.rm=TRUE))
tb14 <- ETS.MSE %>% mutate(
MSE.1 = ifelse(
rank(MSE.1) <= 3,
cell_spec(
paste0(round(MSE.1, 7), ' (rank: ', sprintf('%1.f', rank(MSE.1)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.1, 7), ' (rank: ', sprintf('%1.f', rank(MSE.1)), ')'),
'html', color = 'grey', italic = TRUE)),
MSE.2 = ifelse(
rank(MSE.2) <= 3,
cell_spec(
paste0(round(MSE.2, 7), ' (rank: ', sprintf('%1.f', rank(MSE.2)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(MSE.2, 7), ' (rank: ', sprintf('%1.f', rank(MSE.2)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'MSE of daily Opened and Closed Transaction Orders', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kableExtra::group_rows('AAN', 1, 25, label_row_css = 'background-color: #e68a00; color: #fff;') %>%
kableExtra::group_rows('AAZ', 26, 50, label_row_css = 'background-color: #ff0000; color: #fff;') %>%
kableExtra::group_rows('ANN', 51, 75, label_row_css = 'background-color: #bf80ff; color: #fff;') %>%
kableExtra::group_rows('ANZ', 76, 100, label_row_css = 'background-color: #66ff33; color: #fff;') %>%
kableExtra::group_rows('AZN', 101, 125, label_row_css = 'background-color: #6666ff; color: #fff;') %>%
kableExtra::group_rows('AZZ', 126, 150, label_row_css = 'background-color: #66e0ff; color: #fff;') %>%
kableExtra::group_rows('MAN', 151, 175, label_row_css = 'background-color:#0066ff; color: #fff;') %>%
kableExtra::group_rows('MAZ', 176, 200, label_row_css = 'background-color: #ff9900; color: #fff;') %>%
kableExtra::group_rows('MMN', 201, 225, label_row_css = 'background-color: #33ff33; color: #fff;') %>%
kableExtra::group_rows('MMZ', 226, 250, label_row_css = 'background-color: #339966; color: #fff;') %>%
kableExtra::group_rows('MNN', 251, 275, label_row_css = 'background-color: #5900b3; color: #fff;') %>%
kableExtra::group_rows('MNZ', 276, 300, label_row_css = 'background-color: #269900; color: #fff;') %>%
kableExtra::group_rows('MZN', 301, 325, label_row_css = 'background-color: #808000; color: #fff;') %>%
kableExtra::group_rows('MZZ', 326, 350, label_row_css = 'background-color: #3399ff; color: #fff;') %>%
kableExtra::group_rows('ZAN', 351, 375, label_row_css = 'background-color: #003380; color: #fff;') %>%
kableExtra::group_rows('ZAZ', 376, 400, label_row_css = 'background-color: #804d00; color: #fff;') %>%
kableExtra::group_rows('ZMN', 401, 425, label_row_css = 'background-color: #d279d2; color: #fff;') %>%
kableExtra::group_rows('ZMZ', 426, 450, label_row_css = 'background-color: #666; color: #fff;') %>%
kableExtra::group_rows('ZNN', 451, 475, label_row_css = 'background-color: #ff3377; color: #fff;') %>%
kableExtra::group_rows('ZNZ', 476, 500, label_row_css = 'background-color: #993399; color: #fff;') %>%
kableExtra::group_rows('ZZN', 501, 525, label_row_css = 'background-color: #00a3cc; color: #fff;') %>%
kableExtra::group_rows('ZZZ', 526, 550, label_row_css = 'background-color: #e60000; color: #fff;') %>%
scroll_box(width = '100%', height = '400px')
tb14| Model | Type | MSE.1 | MSE.2 |
|---|---|---|---|
| AAN | |||
| AAN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| AAN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| AAN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| AAN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| AAN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| AAN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| AAN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| AAN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| AAN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| AAN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| AAN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| AAN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| AAN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| AAN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| AAN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| AAN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| AAN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| AAN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| AAN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| AAN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| AAN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| AAN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| AAN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| AAN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| AAN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| AAZ | |||
| AAZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| AAZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| AAZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| AAZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| AAZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| AAZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| AAZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| AAZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| AAZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| AAZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| AAZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| AAZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| AAZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| AAZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| AAZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| AAZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| AAZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| AAZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| AAZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| AAZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| AAZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| AAZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| AAZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| AAZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| AAZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ANN | |||
| ANN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ANN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ANN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ANN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ANN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ANN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ANN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ANN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ANN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ANN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ANN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ANN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ANN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ANN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ANN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ANN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ANN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ANN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ANN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ANN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ANN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ANN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ANN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ANN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ANN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ANZ | |||
| ANZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ANZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ANZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ANZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ANZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ANZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ANZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ANZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ANZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ANZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ANZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ANZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ANZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ANZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ANZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ANZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ANZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ANZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ANZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ANZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ANZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ANZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ANZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ANZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ANZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| AZN | |||
| AZN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| AZN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| AZN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| AZN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| AZN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| AZN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| AZN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| AZN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| AZN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| AZN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| AZN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| AZN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| AZN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| AZN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| AZN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| AZN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| AZN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| AZN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| AZN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| AZN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| AZN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| AZN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| AZN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| AZN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| AZN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| AZZ | |||
| AZZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| AZZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| AZZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| AZZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| AZZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| AZZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| AZZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| AZZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| AZZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| AZZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| AZZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| AZZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| AZZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| AZZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| AZZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| AZZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| AZZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| AZZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| AZZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| AZZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| AZZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| AZZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| AZZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| AZZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| AZZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MAN | |||
| MAN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MAN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MAN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MAN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MAN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MAN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MAN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MAN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MAN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MAN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MAN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MAN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MAN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MAN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MAN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MAN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MAN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MAN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MAN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MAN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MAN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MAN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MAN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MAN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MAN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MAZ | |||
| MAZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MAZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MAZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MAZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MAZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MAZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MAZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MAZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MAZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MAZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MAZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MAZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MAZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MAZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MAZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MAZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MAZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MAZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MAZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MAZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MAZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MAZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MAZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MAZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MAZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MMN | |||
| MMN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MMN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MMN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MMN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MMN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MMN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MMN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MMN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MMN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MMN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MMN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MMN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MMN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MMN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MMN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MMN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MMN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MMN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MMN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MMN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MMN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MMN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MMN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MMN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MMN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MMZ | |||
| MMZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MMZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MMZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MMZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MMZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MMZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MMZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MMZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MMZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MMZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MMZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MMZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MMZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MMZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MMZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MMZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MMZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MMZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MMZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MMZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MMZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MMZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MMZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MMZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MMZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MNN | |||
| MNN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MNN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MNN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MNN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MNN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MNN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MNN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MNN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MNN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MNN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MNN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MNN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MNN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MNN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MNN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MNN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MNN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MNN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MNN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MNN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MNN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MNN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MNN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MNN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MNN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MNZ | |||
| MNZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MNZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MNZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MNZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MNZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MNZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MNZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MNZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MNZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MNZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MNZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MNZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MNZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MNZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MNZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MNZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MNZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MNZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MNZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MNZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MNZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MNZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MNZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MNZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MNZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MZN | |||
| MZN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MZN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MZN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MZN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MZN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MZN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MZN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MZN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MZN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MZN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MZN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MZN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MZN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MZN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MZN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MZN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MZN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MZN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MZN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MZN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MZN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MZN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MZN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MZN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MZN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| MZZ | |||
| MZZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| MZZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| MZZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| MZZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| MZZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| MZZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| MZZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| MZZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| MZZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| MZZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| MZZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| MZZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| MZZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| MZZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| MZZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| MZZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| MZZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| MZZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| MZZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| MZZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| MZZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| MZZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| MZZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| MZZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| MZZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZAN | |||
| ZAN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZAN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZAN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZAN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZAN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZAN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZAN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZAN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZAN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZAN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZAN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZAN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZAN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZAN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZAN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZAN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZAN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZAN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZAN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZAN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZAN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZAN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZAN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZAN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZAN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZAZ | |||
| ZAZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZAZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZAZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZAZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZAZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZAZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZAZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZAZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZAZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZAZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZAZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZAZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZAZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZAZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZAZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZAZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZAZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZAZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZAZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZAZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZAZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZAZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZAZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZAZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZAZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZMN | |||
| ZMN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZMN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZMN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZMN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZMN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZMN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZMN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZMN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZMN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZMN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZMN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZMN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZMN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZMN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZMN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZMN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZMN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZMN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZMN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZMN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZMN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZMN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZMN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZMN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZMN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZMZ | |||
| ZMZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZMZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZMZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZMZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZMZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZMZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZMZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZMZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZMZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZMZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZMZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZMZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZMZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZMZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZMZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZMZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZMZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZMZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZMZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZMZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZMZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZMZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZMZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZMZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZMZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZNN | |||
| ZNN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZNN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZNN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZNN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZNN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZNN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZNN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZNN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZNN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZNN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZNN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZNN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZNN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZNN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZNN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZNN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZNN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZNN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZNN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZNN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZNN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZNN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZNN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZNN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZNN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZNZ | |||
| ZNZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZNZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZNZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZNZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZNZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZNZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZNZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZNZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZNZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZNZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZNZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZNZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZNZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZNZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZNZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZNZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZNZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZNZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZNZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZNZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZNZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZNZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZNZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZNZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZNZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZZN | |||
| ZZN | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZZN | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZZN | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZZN | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZZN | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZZN | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZZN | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZZN | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZZN | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZZN | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZZN | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZZN | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZZN | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZZN | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZZN | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZZN | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZZN | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZZN | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZZN | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZZN | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZZN | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZZN | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZZN | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZZN | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZZN | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
| ZZZ | |||
| ZZZ | ClCl | 0.467076 (rank: 166) | 0.467076 (rank: 166) |
| ZZZ | ClHi | 0.467076 (rank: 166) | 0.8097381 (rank: 386) |
| ZZZ | ClLo | 0.467076 (rank: 166) | 1.0410108 (rank: 496) |
| ZZZ | ClMn | 0.467076 (rank: 166) | 0.6447018 (rank: 276) |
| ZZZ | ClOp | 0.467076 (rank: 166) | 0.4635132 (rank: 56) |
| ZZZ | HiCl | 0.8097381 (rank: 386) | 0.467076 (rank: 166) |
| ZZZ | HiHi | 0.8097381 (rank: 386) | 0.8097381 (rank: 386) |
| ZZZ | HiLo | 0.8097381 (rank: 386) | 1.0410108 (rank: 496) |
| ZZZ | HiMn | 0.8097381 (rank: 386) | 0.6447018 (rank: 276) |
| ZZZ | HiOp | 0.8097381 (rank: 386) | 0.4635132 (rank: 56) |
| ZZZ | LoCl | 1.0410108 (rank: 496) | 0.467076 (rank: 166) |
| ZZZ | LoHi | 1.0410108 (rank: 496) | 0.8097381 (rank: 386) |
| ZZZ | LoLo | 1.0410108 (rank: 496) | 1.0410108 (rank: 496) |
| ZZZ | LoMn | 1.0410108 (rank: 496) | 0.6447018 (rank: 276) |
| ZZZ | LoOp | 1.0410108 (rank: 496) | 0.4635132 (rank: 56) |
| ZZZ | MnCl | 0.6447018 (rank: 276) | 0.467076 (rank: 166) |
| ZZZ | MnHi | 0.6447018 (rank: 276) | 0.8097381 (rank: 386) |
| ZZZ | MnLo | 0.6447018 (rank: 276) | 1.0410108 (rank: 496) |
| ZZZ | MnMn | 0.6447018 (rank: 276) | 0.6447018 (rank: 276) |
| ZZZ | MnOp | 0.6447018 (rank: 276) | 0.4635132 (rank: 56) |
| ZZZ | OpCl | 0.4635132 (rank: 56) | 0.467076 (rank: 166) |
| ZZZ | OpHi | 0.4635132 (rank: 56) | 0.8097381 (rank: 386) |
| ZZZ | OpLo | 0.4635132 (rank: 56) | 1.0410108 (rank: 496) |
| ZZZ | OpMn | 0.4635132 (rank: 56) | 0.6447018 (rank: 276) |
| ZZZ | OpOp | 0.4635132 (rank: 56) | 0.4635132 (rank: 56) |
Source : Binary.com Interview Q1 (Extention)
From above MSE comparison with intraday-dataset, we know that the intraday data will be more accurate than just daily dataset.
5.2.2 Interday auto.arima Model
- Forecasting: Principles and Practice - 11.1 Complex seasonality
- Forecasting: Principles and Practice - 12.1 Weekly, daily and sub-daily data
ar.fls <- list.files('data', pattern = '^fundAutoArima')
ARIMA.MSE <- llply(ar.fls, function(x) {
nm <- x %>%
str_replace_all('.rds', '') %>%
substring(nchar(.) - 3)
y <- paste0('data/', x) %>%
read_rds
data.frame(Model = 'auto.arima', Type = nm, y) %>% as_tibble
}) %>% bind_rows %>%
mutate(index = Date) %>%
dplyr::select(index, Model, Type, Point.Forecast, forClose,
USDJPY.Open, USDJPY.High, USDJPY.Low, USDJPY.Close,
-Date)
ARIMA.MSE %<>% mutate(
MSE.1 = case_when(
substr(Type, 1, 2) == 'OP' ~ mean((Point.Forecast - USDJPY.Open)^2),
substr(Type, 1, 2) == 'HI' ~ mean((Point.Forecast - USDJPY.High)^2),
substr(Type, 1, 2) == 'MN' ~ mean((Point.Forecast - (USDJPY.High + USDJPY.Low)/2)^2),
substr(Type, 1, 2) == 'LO' ~ mean((Point.Forecast - USDJPY.Low)^2),
substr(Type, 1, 2) == 'CL' ~ mean((Point.Forecast - USDJPY.Close)^2)),
MSE.2 = case_when(
substr(Type, 3, 4) == 'OP' ~ mean((Point.Forecast - USDJPY.Open)^2),
substr(Type, 3, 4) == 'HI' ~ mean((Point.Forecast - USDJPY.High)^2),
substr(Type, 3, 4) == 'MN' ~ mean((Point.Forecast - (USDJPY.High + USDJPY.Low)/2)^2),
substr(Type, 3, 4) == 'LO' ~ mean((Point.Forecast - USDJPY.Low)^2),
substr(Type, 3, 4) == 'CL' ~ mean((Point.Forecast - USDJPY.Close)^2)))
tb15 <- ARIMA.MSE %>%
ddply(.(Model), summarise,
MSE.1 = mean(MSE.1, na.rm=TRUE),
MSE.2 = mean(MSE.2, na.rm=TRUE)) %>%
arrange(MSE.1, MSE.2) %>%
kable(caption = 'MSE of daily Opened and Closed Transaction Orders') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
tb15| Model | MSE.1 | MSE.2 |
|---|---|---|
| auto.arima | 0.6962568 | 0.7515629 |
6 Conclusion
6.1 Summary
From the backtest, we concludes that high-frequency-trading 1 min per unit (ETS:0.46 and auto.arima:0.69) more accurate than interday-trading 1 day per unit.
High- and Low-Frequency Correlations in European Government Bond Spreads and Their Macroeconomic Drivers introduce… suggest… DCC-MIDAS etc. Due to heavily .
By refer to section [#713_Unexpected_Error], here I omitted the data from year 2018-01-01 to 2018-07-09 but the outcome is same. Here I forced to omit the mentioned dataset.
6.2 Dataset Filtering
6.2.1 Overall Dataset from 2015-01-05 to 2017-12-31
if(!exists('seasonal_m1')) {
seasonal_m1 <- read_rds('data/fx/USDJPY/seasonal_m1.rds')}
ftl1 <- seasonal_m1 %>%
filter(index <= as_date('2017-12-31'))
ftl1 %<>% data.table()
m.op <- ftl1[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.hi <- ftl1[, {
high = high
high.Point.Forecast = high.Point.Forecast
.SD[, .(.N, high.mape = MAPE(high, high.Point.Forecast),
high.smape = SMAPE(high, high.Point.Forecast),
high.mse = MSE(high, high.Point.Forecast),
high.rmse = RMSE(high, high.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.lo <- ftl1[, {
low = low
low.Point.Forecast = low.Point.Forecast
.SD[, .(.N, low.mape = MAPE(low, low.Point.Forecast),
low.smape = SMAPE(low, low.Point.Forecast),
low.mse = MSE(low, low.Point.Forecast),
low.rmse = RMSE(low, low.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
m.cl <- ftl1[, {
close = close
close.Point.Forecast = close.Point.Forecast
.SD[, .(.N, close.mape = MAPE(close, close.Point.Forecast),
close.smape = SMAPE(close, close.Point.Forecast),
close.mse = MSE(close, close.Point.Forecast),
close.rmse = RMSE(close, close.Point.Forecast)),
by=.(Model, Period)]}][order(Model, Period), ]
ftl_dat1 <- join_all(list(m.op, m.hi, m.lo, m.cl)) %>% tibbletb16 <- ftl_dat1 %>%
mutate(
open.mape = ifelse(
rank(open.mape) <= 3,
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.smape = ifelse(
rank(open.smape) <= 3,
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.mse = ifelse(
rank(open.mse) <= 3,
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
open.rmse = ifelse(
rank(open.rmse) <= 3,
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mape = ifelse(
rank(high.mape) <= 3,
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.smape = ifelse(
rank(high.smape) <= 3,
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mse = ifelse(
rank(high.mse) <= 3,
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.rmse = ifelse(
rank(high.rmse) <= 3,
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mape = ifelse(
rank(low.mape) <= 3,
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.smape = ifelse(
rank(low.smape) <= 3,
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mse = ifelse(
rank(low.mse) <= 3,
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.rmse = ifelse(
rank(low.rmse) <= 3,
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mape = ifelse(
rank(close.mape) <= 3,
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.smape = ifelse(
rank(close.smape) <= 3,
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mse = ifelse(
rank(close.mse) <= 3,
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.rmse = ifelse(
rank(close.rmse) <= 3,
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min summarised to 1 day per unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
column_spec(3, background = 'LightSlateGrey') %>%
column_spec(4, background = 'LightGray') %>%
column_spec(5, background = 'Gainsboro') %>%
column_spec(6, background = 'LightGray') %>%
column_spec(7, background = 'Gainsboro') %>%
column_spec(8, background = 'LightGray') %>%
column_spec(9, background = 'Gainsboro') %>%
column_spec(10, background = 'LightGray') %>%
column_spec(11, background = 'Gainsboro') %>%
column_spec(12, background = 'LightGray') %>%
column_spec(13, background = 'Gainsboro') %>%
column_spec(14, background = 'LightGray') %>%
column_spec(15, background = 'Gainsboro') %>%
column_spec(16, background = 'LightGray') %>%
column_spec(17, background = 'Gainsboro') %>%
column_spec(18, background = 'LightGray') %>%
column_spec(19, background = 'Gainsboro') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb16| Model | Period | N | open.mape | open.smape | open.mse | open.rmse | high.mape | high.smape | high.mse | high.rmse | low.mape | low.smape | low.mse | low.rmse | close.mape | close.smape | close.mse | close.rmse |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 1107360 | 0.0028697 (rank: 2) | 0.0028715 (rank: 2) | 0.2472555 (rank: 2) | 0.4972479 (rank: 2) | 0.0028737 (rank: 2) | 0.0028755 (rank: 2) | 0.2475336 (rank: 2) | 0.4975274 (rank: 2) | 0.0028783 (rank: 2) | 0.0028801 (rank: 2) | 0.2467347 (rank: 2) | 0.4967239 (rank: 2) | 0.0028641 (rank: 3) | 0.0028659 (rank: 3) | 0.2446939 (rank: 2) | 0.4946655 (rank: 2) |
| tbats | dy.wk | 1107360 | 0.0028955 (rank: 3) | 0.0028974 (rank: 3) | 0.2522675 (rank: 3) | 0.5022624 (rank: 3) | 0.0028838 (rank: 3) | 0.0028858 (rank: 3) | 0.250246 (rank: 3) | 0.500246 (rank: 3) | 0.0028883 (rank: 3) | 0.0028901 (rank: 3) | 0.2534677 (rank: 4) | 0.5034558 (rank: 4) | 0.0029303 (rank: 4) | 0.0029325 (rank: 4) | 0.2632625 (rank: 7) | 0.5130911 (rank: 7) |
| tbats | dy.wk.mo | 1095840 | 0.0029009 (rank: 4) | 0.0029033 (rank: 4) | 0.2612362 (rank: 7) | 0.5111127 (rank: 7) | 0.0028944 (rank: 4) | 0.002896 (rank: 4) | 0.2547063 (rank: 4) | 0.5046843 (rank: 4) | 0.0029111 (rank: 4) | 0.0029129 (rank: 4) | 0.2524913 (rank: 3) | 0.5024851 (rank: 3) | 0.0028632 (rank: 2) | 0.002865 (rank: 2) | 0.2471047 (rank: 3) | 0.4970963 (rank: 3) |
| tbats | dy.yr | 1107360 | 0.0028639 (rank: 1) | 0.0028657 (rank: 1) | 0.2463068 (rank: 1) | 0.496293 (rank: 1) | 0.0028654 (rank: 1) | 0.0028672 (rank: 1) | 0.2467196 (rank: 1) | 0.4967088 (rank: 1) | 0.0028677 (rank: 1) | 0.0028693 (rank: 1) | 0.243529 (rank: 1) | 0.4934866 (rank: 1) | 0.0028541 (rank: 1) | 0.0028559 (rank: 1) | 0.243923 (rank: 1) | 0.4938856 (rank: 1) |
| ts | mo.1440 | 1107360 | 0.0029713 (rank: 7) | 0.0029726 (rank: 7) | 0.2600749 (rank: 6) | 0.5099754 (rank: 6) | 0.0029619 (rank: 8) | 0.0029634 (rank: 8) | 0.2584294 (rank: 7) | 0.5083595 (rank: 7) | 0.0029577 (rank: 6) | 0.0029591 (rank: 6) | 0.2556744 (rank: 7) | 0.5056425 (rank: 7) | 0.002972 (rank: 7) | 0.0029733 (rank: 7) | 0.2590251 (rank: 6) | 0.5089451 (rank: 6) |
| ts | mo.7200 | 244800 | 0.0034764 (rank: 10) | 0.0034756 (rank: 10) | 0.3134664 (rank: 10) | 0.5598807 (rank: 10) | 0.0035018 (rank: 10) | 0.0035011 (rank: 10) | 0.3146787 (rank: 10) | 0.5609623 (rank: 10) | 0.0034669 (rank: 10) | 0.0034659 (rank: 10) | 0.3119626 (rank: 9) | 0.5585361 (rank: 9) | 0.0034906 (rank: 10) | 0.0034897 (rank: 10) | 0.3142609 (rank: 9) | 0.5605898 (rank: 9) |
| ts | qt.1440 | 1107360 | 0.0029539 (rank: 5) | 0.0029554 (rank: 5) | 0.2565877 (rank: 4) | 0.5065449 (rank: 4) | 0.0029549 (rank: 6) | 0.0029564 (rank: 6) | 0.2568182 (rank: 6) | 0.5067723 (rank: 6) | 0.0029573 (rank: 5) | 0.0029587 (rank: 5) | 0.2554396 (rank: 5) | 0.5054103 (rank: 5) | 0.0029541 (rank: 5) | 0.0029556 (rank: 5) | 0.2554277 (rank: 4) | 0.5053986 (rank: 4) |
| ts | qt.7200 | 223200 | 0.0034844 (rank: 11) | 0.0034841 (rank: 11) | 0.3156878 (rank: 11) | 0.561861 (rank: 11) | 0.0035078 (rank: 11) | 0.0035075 (rank: 11) | 0.3167276 (rank: 11) | 0.5627856 (rank: 11) | 0.0034754 (rank: 11) | 0.003475 (rank: 11) | 0.3144045 (rank: 10) | 0.5607179 (rank: 10) | 0.0034988 (rank: 11) | 0.0034984 (rank: 11) | 0.3168899 (rank: 10) | 0.5629298 (rank: 10) |
| ts | wk.1440 | 1107360 | 0.003094 (rank: 9) | 0.0030953 (rank: 9) | 0.275519 (rank: 8) | 0.524899 (rank: 8) | 0.0030763 (rank: 9) | 0.0030778 (rank: 9) | 0.2697875 (rank: 9) | 0.5194107 (rank: 9) | 0.0030852 (rank: 9) | 0.0030864 (rank: 9) | 0.271656 (rank: 8) | 0.5212063 (rank: 8) | 0.0030826 (rank: 9) | 0.0030839 (rank: 9) | 0.2714963 (rank: 8) | 0.5210531 (rank: 8) |
| ts | wk.7200 | 5536800 | 0.0029907 (rank: 8) | 0.0029907 (rank: 8) | 0.3108382 (rank: 9) | 0.5575287 (rank: 9) | 0.0029087 (rank: 5) | 0.0029104 (rank: 5) | 0.2606856 (rank: 8) | 0.5105738 (rank: 8) | 0.0030497 (rank: 8) | 0.003049 (rank: 8) | 0.3365699 (rank: 12) | 0.5801465 (rank: 12) | 0.0030335 (rank: 8) | 0.0030308 (rank: 8) | 0.3546758 (rank: 12) | 0.5955467 (rank: 12) |
| ts | yr.1440 | 1107360 | 0.002954 (rank: 6) | 0.0029555 (rank: 6) | 0.2566071 (rank: 5) | 0.506564 (rank: 5) | 0.002955 (rank: 7) | 0.0029565 (rank: 7) | 0.2567897 (rank: 5) | 0.5067442 (rank: 5) | 0.0029581 (rank: 7) | 0.0029595 (rank: 7) | 0.2555165 (rank: 6) | 0.5054864 (rank: 6) | 0.0029543 (rank: 6) | 0.0029557 (rank: 6) | 0.255448 (rank: 5) | 0.5054187 (rank: 5) |
| ts | yr.7200 | 208800 | 0.0036239 (rank: 12) | 0.0036236 (rank: 12) | 0.3342637 (rank: 12) | 0.5781554 (rank: 12) | 0.0036485 (rank: 12) | 0.0036482 (rank: 12) | 0.3353777 (rank: 12) | 0.5791181 (rank: 12) | 0.0036111 (rank: 12) | 0.0036106 (rank: 12) | 0.3327021 (rank: 11) | 0.5768033 (rank: 11) | 0.0036356 (rank: 12) | 0.0036352 (rank: 12) | 0.335306 (rank: 11) | 0.5790561 (rank: 11) |
Above table summarized the total observations with mape, smape, mse and rmse values (which is not nested summarize not daily settlement for P&L).
6.2.2 Daily Dataset from 2015-01-05 to 2017-12-31
open.accr <- ftl1[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
high.accr <- ftl1[, {
high = high
high.Point.Forecast = high.Point.Forecast
.SD[, .(.N, high.mape = MAPE(high, high.Point.Forecast),
high.smape = SMAPE(high, high.Point.Forecast),
high.mse = MSE(high, high.Point.Forecast),
high.rmse = RMSE(high, high.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
low.accr <- ftl1[, {
low = low
low.Point.Forecast = low.Point.Forecast
.SD[, .(.N, low.mape = MAPE(low, low.Point.Forecast),
low.smape = SMAPE(low, low.Point.Forecast),
low.mse = MSE(low, low.Point.Forecast),
low.rmse = RMSE(low, low.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
close.accr <- ftl1[, {
close = close
close.Point.Forecast = close.Point.Forecast
.SD[, .(.N, close.mape = MAPE(close, close.Point.Forecast),
close.smape = SMAPE(close, close.Point.Forecast),
close.mse = MSE(close, close.Point.Forecast),
close.rmse = RMSE(close, close.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
open.sm <- open.accr[, list(open.mape = mean(open.mape),
open.smape = mean(open.smape),
open.mse = mean(open.mse),
open.rmse = mean(open.rmse)),
by=.(Model, Period)]
high.sm <- high.accr[, list(high.mape = mean(high.mape),
high.smape = mean(high.smape),
high.mse = mean(high.mse),
high.rmse = mean(high.rmse)),
by=.(Model, Period)]
low.sm <- low.accr[, list(low.mape = mean(low.mape),
low.smape = mean(low.smape),
low.mse = mean(low.mse),
low.rmse = mean(low.rmse)),
by=.(Model, Period)]
close.sm <- close.accr[, list(close.mape = mean(close.mape),
close.smape = mean(close.smape),
close.mse = mean(close.mse),
close.rmse = mean(close.rmse)),
by=.(Model, Period)]
ftl_dat2 <- join_all(list(open.sm, high.sm, low.sm, close.sm)) %>%
tibbletb17 <- ftl_dat2 %>%
mutate(
open.mape = ifelse(
rank(open.mape) <= 3,
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mape, 7), ' (rank: ', sprintf('%1.f', rank(open.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.smape = ifelse(
rank(open.smape) <= 3,
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.smape, 7), ' (rank: ', sprintf('%1.f', rank(open.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
open.mse = ifelse(
rank(open.mse) <= 3,
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.mse, 7), ' (rank: ', sprintf('%1.f', rank(open.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
open.rmse = ifelse(
rank(open.rmse) <= 3,
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(open.rmse, 7), ' (rank: ', sprintf('%1.f', rank(open.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mape = ifelse(
rank(high.mape) <= 3,
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mape, 7), ' (rank: ', sprintf('%1.f', rank(high.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.smape = ifelse(
rank(high.smape) <= 3,
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.smape, 7), ' (rank: ', sprintf('%1.f', rank(high.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
high.mse = ifelse(
rank(high.mse) <= 3,
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.mse, 7), ' (rank: ', sprintf('%1.f', rank(high.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
high.rmse = ifelse(
rank(high.rmse) <= 3,
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(high.rmse, 7), ' (rank: ', sprintf('%1.f', rank(high.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mape = ifelse(
rank(low.mape) <= 3,
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mape, 7), ' (rank: ', sprintf('%1.f', rank(low.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.smape = ifelse(
rank(low.smape) <= 3,
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.smape, 7), ' (rank: ', sprintf('%1.f', rank(low.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
low.mse = ifelse(
rank(low.mse) <= 3,
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.mse, 7), ' (rank: ', sprintf('%1.f', rank(low.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
low.rmse = ifelse(
rank(low.rmse) <= 3,
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(low.rmse, 7), ' (rank: ', sprintf('%1.f', rank(low.rmse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mape = ifelse(
rank(close.mape) <= 3,
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mape, 7), ' (rank: ', sprintf('%1.f', rank(close.mape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.smape = ifelse(
rank(close.smape) <= 3,
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.smape, 7), ' (rank: ', sprintf('%1.f', rank(close.smape)), ')'),
'html', color = 'grey', italic = TRUE)),
close.mse = ifelse(
rank(close.mse) <= 3,
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.mse, 7), ' (rank: ', sprintf('%1.f', rank(close.mse)), ')'),
'html', color = 'grey', italic = TRUE)),
close.rmse = ifelse(
rank(close.rmse) <= 3,
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'darkgoldenrod', bold = TRUE),
cell_spec(
paste0(round(close.rmse, 7), ' (rank: ', sprintf('%1.f', rank(close.rmse)), ')'),
'html', color = 'grey', italic = TRUE))) %>%
kbl('html', caption = 'Comparison of Models (1 min summarised to 1 day per unit)', escape = FALSE) %>%
## https://www.w3schools.com/cssref/css_colors.asp
row_spec(0, background = 'DimGrey') %>%
column_spec(1, background = 'CornflowerBlue') %>%
column_spec(2, background = 'DarkGrey') %>%
#column_spec(3, background = 'LightSlateGrey') %>%
column_spec(3, background = 'LightGray') %>%
column_spec(4, background = 'Gainsboro') %>%
column_spec(5, background = 'LightGray') %>%
column_spec(6, background = 'Gainsboro') %>%
column_spec(7, background = 'LightGray') %>%
column_spec(8, background = 'Gainsboro') %>%
column_spec(9, background = 'LightGray') %>%
column_spec(10, background = 'Gainsboro') %>%
column_spec(11, background = 'LightGray') %>%
column_spec(12, background = 'Gainsboro') %>%
column_spec(13, background = 'LightGray') %>%
column_spec(14, background = 'Gainsboro') %>%
column_spec(15, background = 'LightGray') %>%
column_spec(16, background = 'Gainsboro') %>%
column_spec(17, background = 'LightGray') %>%
column_spec(18, background = 'Gainsboro') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
scroll_box(width = '100%')#, height = '400px')
tb17| Model | Period | open.mape | open.smape | open.mse | open.rmse | high.mape | high.smape | high.mse | high.rmse | low.mape | low.smape | low.mse | low.rmse | close.mape | close.smape | close.mse | close.rmse |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 0.0031798 (rank: 2) | 0.0031822 (rank: 2) | 0.3086508 (rank: 2) | 0.4131941 (rank: 2) | 0.0031952 (rank: 2) | 0.0031978 (rank: 2) | 0.3113727 (rank: 2) | 0.4148375 (rank: 2) | 0.0031943 (rank: 3) | 0.0031963 (rank: 3) | 0.3062676 (rank: 2) | 0.4146386 (rank: 3) | 0.0031765 (rank: 3) | 0.0031787 (rank: 3) | 0.3051462 (rank: 3) | 0.4128326 (rank: 3) |
| tbats | dy.wk | 0.0032293 (rank: 4) | 0.0032321 (rank: 4) | 0.3236162 (rank: 7) | 0.4187807 (rank: 4) | 0.0032012 (rank: 3) | 0.0032039 (rank: 3) | 0.3131142 (rank: 3) | 0.4153888 (rank: 3) | 0.0031922 (rank: 2) | 0.0031943 (rank: 2) | 0.3104748 (rank: 3) | 0.4146143 (rank: 2) | 0.0032804 (rank: 7) | 0.003283 (rank: 7) | 0.3329877 (rank: 8) | 0.4252121 (rank: 7) |
| tbats | dy.yr | 0.0031794 (rank: 1) | 0.0031819 (rank: 1) | 0.3079539 (rank: 1) | 0.4128712 (rank: 1) | 0.0031843 (rank: 1) | 0.0031869 (rank: 1) | 0.3105311 (rank: 1) | 0.4134938 (rank: 1) | 0.0031787 (rank: 1) | 0.0031806 (rank: 1) | 0.3006453 (rank: 1) | 0.4128344 (rank: 1) | 0.0031654 (rank: 2) | 0.0031677 (rank: 2) | 0.3036 (rank: 1) | 0.4114234 (rank: 2) |
| ts | mo.1440 | 0.003268 (rank: 7) | 0.00327 (rank: 7) | 0.3193867 (rank: 6) | 0.4240055 (rank: 7) | 0.003274 (rank: 8) | 0.0032763 (rank: 8) | 0.3219065 (rank: 7) | 0.4247684 (rank: 8) | 0.0032505 (rank: 6) | 0.0032523 (rank: 6) | 0.3120875 (rank: 6) | 0.4219785 (rank: 6) | 0.0032666 (rank: 6) | 0.0032685 (rank: 6) | 0.3167097 (rank: 6) | 0.4238872 (rank: 6) |
| ts | mo.7200 | 0.0041186 (rank: 11) | 0.0041147 (rank: 11) | 0.425753 (rank: 11) | 0.5564735 (rank: 11) | 0.0041905 (rank: 11) | 0.0041868 (rank: 11) | 0.4366597 (rank: 11) | 0.5650381 (rank: 11) | 0.0040769 (rank: 11) | 0.0040725 (rank: 11) | 0.4221267 (rank: 11) | 0.5517966 (rank: 11) | 0.0041607 (rank: 11) | 0.0041564 (rank: 11) | 0.4379246 (rank: 11) | 0.5616704 (rank: 11) |
| ts | qt.1440 | 0.0032537 (rank: 5) | 0.0032559 (rank: 5) | 0.3165277 (rank: 3) | 0.4223453 (rank: 5) | 0.0032589 (rank: 6) | 0.0032613 (rank: 6) | 0.3186365 (rank: 6) | 0.4229761 (rank: 6) | 0.0032501 (rank: 5) | 0.0032518 (rank: 5) | 0.3116999 (rank: 4) | 0.4219301 (rank: 5) | 0.0032516 (rank: 4) | 0.0032536 (rank: 4) | 0.3136698 (rank: 4) | 0.4221424 (rank: 4) |
| ts | qt.7200 | 0.004058 (rank: 10) | 0.0040546 (rank: 10) | 0.42255 (rank: 10) | 0.5479559 (rank: 10) | 0.004129 (rank: 10) | 0.0041259 (rank: 10) | 0.4333607 (rank: 10) | 0.5565739 (rank: 10) | 0.0039968 (rank: 10) | 0.0039929 (rank: 10) | 0.4190357 (rank: 10) | 0.5412921 (rank: 10) | 0.0040893 (rank: 10) | 0.0040855 (rank: 10) | 0.4356525 (rank: 10) | 0.5524039 (rank: 10) |
| ts | wk.1440 | 0.0033941 (rank: 9) | 0.0033961 (rank: 9) | 0.335421 (rank: 8) | 0.4388743 (rank: 9) | 0.0033706 (rank: 9) | 0.0033729 (rank: 9) | 0.330303 (rank: 9) | 0.4356482 (rank: 9) | 0.0033746 (rank: 8) | 0.0033762 (rank: 8) | 0.3273219 (rank: 8) | 0.4362639 (rank: 8) | 0.0033759 (rank: 9) | 0.0033779 (rank: 9) | 0.3303105 (rank: 7) | 0.4365981 (rank: 9) |
| ts | wk.7200 | 0.0033234 (rank: 8) | 0.003324 (rank: 8) | 0.374078 (rank: 9) | 0.4311754 (rank: 8) | 0.0032445 (rank: 5) | 0.0032467 (rank: 5) | 0.32989 (rank: 8) | 0.4206439 (rank: 5) | 0.0033927 (rank: 9) | 0.0033931 (rank: 9) | 0.4060808 (rank: 9) | 0.4394059 (rank: 9) | 0.0033423 (rank: 8) | 0.0033406 (rank: 8) | 0.4049183 (rank: 9) | 0.4323124 (rank: 8) |
| ts | yr.1440 | 0.0032538 (rank: 6) | 0.003256 (rank: 6) | 0.3165405 (rank: 4) | 0.4223546 (rank: 6) | 0.0032591 (rank: 7) | 0.0032615 (rank: 7) | 0.3185936 (rank: 5) | 0.4229942 (rank: 7) | 0.0032507 (rank: 7) | 0.0032525 (rank: 7) | 0.3117464 (rank: 5) | 0.4220256 (rank: 7) | 0.0032518 (rank: 5) | 0.0032538 (rank: 5) | 0.3136856 (rank: 5) | 0.4221609 (rank: 5) |
| ts | yr.7200 | 0.0042881 (rank: 12) | 0.0042843 (rank: 12) | 0.4553046 (rank: 12) | 0.5785254 (rank: 12) | 0.0043671 (rank: 12) | 0.0043636 (rank: 12) | 0.467057 (rank: 12) | 0.5881937 (rank: 12) | 0.0042393 (rank: 12) | 0.004235 (rank: 12) | 0.4522995 (rank: 12) | 0.5732734 (rank: 12) | 0.0043391 (rank: 12) | 0.0043348 (rank: 12) | 0.4701278 (rank: 12) | 0.5850767 (rank: 12) |
| tbats | dy.wk.mo | 0.003199 (rank: 3) | 0.0032018 (rank: 3) | 0.3182763 (rank: 5) | 0.4154379 (rank: 3) | 0.0032051 (rank: 4) | 0.0032076 (rank: 4) | 0.3162797 (rank: 4) | 0.416051 (rank: 4) | 0.0032332 (rank: 4) | 0.0032355 (rank: 4) | 0.31388 (rank: 7) | 0.4190098 (rank: 4) | 0.0031597 (rank: 1) | 0.0031621 (rank: 1) | 0.3038012 (rank: 2) | 0.4105265 (rank: 1) |
Above table summarized the daily mape, smape, mse and rmse values and then summarized again the models (which is nested summarize due to daily settlement for P&L).
- Time Series Forecasting, a Summarize of Data visualization and prediction
- Time Series Analysis and Forecasting with the TSstudio Package
sarimax, tbats with xreg I will also compare the fracdiff() models.
7 Appendix
7.1 Blooper
7.1.1 Efficiency
Efficiency
There cost alot of time for couple models comparison.
# Test the efficiency
> dim(data_m1)
[1] 1324800 5
> microbenchmark(data_m1$index[1], tidyquant::FIRST(data_m1$index), tail(data_m1$index, 1), data_m1$index %>% .[1], data_m1$index %>% (tidyquant::FIRST), data_m1$index %>% tail(1))
Unit: microseconds
expr min lq mean median uq max neval
data_m1$index[1] 8.8 10.40 16.352 11.50 14.20 106.9 100
tidyquant::FIRST(data_m1$index) 34.4 41.25 140.854 46.30 65.15 7256.6 100
tail(data_m1$index, 1) 20.3 24.25 39.063 27.80 36.45 180.4 100
data_m1$index %>% .[1] 12.2 14.60 23.498 15.85 18.70 229.3 100
data_m1$index %>% (tidyquant::FIRST) 39.7 44.05 67.244 50.25 62.60 694.6 100
data_m1$index %>% tail(1) 25.0 30.60 64.955 36.40 57.65 613.7 100
# Test the efficiency
> system.time({
+ smp <- data_m1 %>%
+ tk_xts(silent = TRUE);
+ dt %<>% as_date;
+ smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))];
+
+ mts <- smp %>%
+ msts(seasonal.periods = c(1440, nrow(smp)))
+ })
user system elapsed
0.63 0.09 1.16
> system.time({
+ smp <- tk_xts(data_m1, silent = TRUE);
+ dt %<>% as_date;
+ smp <- smp[paste0(dt %m-% months(3) + seconds(59), '/', dt + seconds(59))];
+
+ mts <- msts(smp, seasonal.periods = c(1440, nrow(smp)))
+ })
user system elapsed
0.16 0.06 0.42
# Test the efficiency
> microbenchmark(
+ as_tibble(matrix(weekdays(unique(na.omit(data.table(data_m1))[weekdays(index) %in% c('Saturday', 'Sunday')]$index)), byrow = TRUE, ncol = 6)),
+ as_tibble(matrix(weekdays(as_date(data_m1$index))[weekdays(as_date(data_m1$index)) %in% c('Saturday', 'Sunday')], byrow = TRUE, ncol = 6))
+ )
Unit: seconds
expr
as_tibble(matrix(weekdays(unique(na.omit(data.table(data_m1))[weekdays(index) %in% c("Saturday", "Sunday")]$index)), byrow = TRUE, ncol = 6))
as_tibble(matrix(weekdays(as_date(data_m1$index))[weekdays(as_date(data_m1$index)) %in% c("Saturday", "Sunday")], byrow = TRUE, ncol = 6))
min lq mean median uq max neval
4.923539 5.102061 5.388813 5.368958 5.552245 6.816211 100
10.182849 10.652719 11.118986 11.026882 11.546361 13.484108 100## https://stackoverflow.com/questions/7014387/whats-the-difference-between-1l-and-1
microbenchmark(seq(1L, 100000000L), seq(1, 100000000), seq(1L, 1e+08), seq(1, 1e+08L), seq(1L, 10L^8L), seq(1, 10^8))## Unit: microseconds
## expr min lq mean median uq max neval
## seq(1L, 100000000L) 5.3 5.5 7.184 5.90 6.80 39.5 100
## seq(1, 1e+08) 5.2 5.5 6.646 5.80 6.40 53.1 100
## seq(1L, 1e+08) 5.1 5.5 6.860 5.80 6.85 37.3 100
## seq(1, 100000000L) 5.3 5.6 7.072 5.90 6.90 30.3 100
## seq(1L, 10L^8L) 5.6 6.0 8.567 6.35 7.10 90.1 100
## seq(1, 10^8) 5.6 5.9 6.992 6.30 7.60 13.7 1007.1.2 Small Mistake
Small Mistake
Here I noticed that there have transactions in Saturday and Sunday as show below when I continue R&D after 2 years from 2018 How Do Orders Execute Over The Weekend?. It is not a big problem since this paper only compare the models and choose the best fit model for high-frequency-trading.
dt_data_m1 <- na.omit(data.table(data_m1))
rm(data_m1)
## date breakdown
dtb <- as_tibble(matrix(unique(as.character(as_date(dt_data_m1$index))), byrow = TRUE, ncol = 6)) %>% mutate_if(is.character, as_date)## Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if `.name_repair` is omitted as of tibble 2.0.0.
## Using compatibility `.name_repair`.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.dtb %>%
mutate(dif = as.numeric(V1 - lag(V1))) %>%
dplyr::filter(dif != 7)## # A tibble: 4 x 7
## V1 V2 V3 V4 V5 V6 dif
## <date> <date> <date> <date> <date> <date> <dbl>
## 1 2016-12-27 2016-12-28 2016-12-29 2016-12-30 2016-12-31 2017-01-01 8
## 2 2017-01-09 2017-01-10 2017-01-11 2017-01-12 2017-01-13 2017-01-14 6
## 3 2017-12-26 2017-12-27 2017-12-28 2017-12-29 2017-12-30 2017-12-31 8
## 4 2018-01-08 2018-01-09 2018-01-10 2018-01-11 2018-01-12 2018-01-13 6## weekdays breakdown
wkb <- dtb %>%
mutate_if(is.Date, weekdays) %>% mutate_if(is.character, as.factor)
wkb #%>% ## # A tibble: 183 x 6
## V1 V2 V3 V4 V5 V6
## <fct> <fct> <fct> <fct> <fct> <fct>
## 1 Monday Tuesday Wednesday Thursday Friday Saturday
## 2 Monday Tuesday Wednesday Thursday Friday Saturday
## 3 Monday Tuesday Wednesday Thursday Friday Saturday
## 4 Monday Tuesday Wednesday Thursday Friday Saturday
## 5 Monday Tuesday Wednesday Thursday Friday Saturday
## 6 Monday Tuesday Wednesday Thursday Friday Saturday
## 7 Monday Tuesday Wednesday Thursday Friday Saturday
## 8 Monday Tuesday Wednesday Thursday Friday Saturday
## 9 Monday Tuesday Wednesday Thursday Friday Saturday
## 10 Monday Tuesday Wednesday Thursday Friday Saturday
## # ... with 173 more rows# dplyr::filter(V1 != 'Monday')7.1.3 Unexpected Error
7.1.3.0.1 Open Price
## Due to the low precision and low accuracy, here I plot the graph and rerun the code to check the models.
yr_2018 <- data.table(seasonal_m1)[as_date(index) > as_date('2017-12-31')]
dy.qt_dy.yr_2018 <- yr_2018[Model == 'tbats' & Period %in% c('dy.qt', 'dy.yr')]
plt_s1 <- yr_2018[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
plt_s2 <- dy.qt_dy.yr_2018[, {
open = open
open.Point.Forecast = open.Point.Forecast
.SD[, .(.N, open.mape = MAPE(open, open.Point.Forecast),
open.smape = SMAPE(open, open.Point.Forecast),
open.mse = MSE(open, open.Point.Forecast),
open.rmse = RMSE(open, open.Point.Forecast)),
by={index=as_date(index)}]},
by=.(Model, Period)]
## ------------------------------------------
##modify dataset
yr_2018 %<>%
tidyr::unite(Model, Model:Period) %>%
data.table
prc <- unique(yr_2018[, .(index, open, high, low, close)])
prc <- prc[, Model := 'Market.Price'][]
yr_2018 <- yr_2018[, (c('open', 'high', 'low', 'close')) := NULL]
names(yr_2018) <- c('index', 'Model', 'open', 'high', 'low', 'close')
yr_2018 <- rbind(yr_2018, prc)
yr_2018 <- data.table(yr_2018)[order(index)]
rm(prc)
mDT <- yr_2018 %>% pivot_longer(!c(index, Model), names_to = 'Variable', values_to = 'Price')
mDT %<>%
tidyr::unite(Model, Model:Variable) %>%
data.table
## ------------------------------------------
plt_s1 %>%
kbl('html', caption = 'Data Sample', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| Model | Period | index | N | open.mape | open.smape | open.mse | open.rmse |
|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.qt | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.qt | 2018-01-05 | 1440 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| tbats | dy.qt | 2018-01-06 | 1 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| tbats | dy.qt | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050751 | 0.4528522 |
| tbats | dy.qt | 2018-01-09 | 1440 | 0.0012943 | 0.0012931 | 0.0419181 | 0.2047390 |
| tbats | dy.qt | 2018-01-10 | 1440 | 0.0073048 | 0.0073400 | 0.8879488 | 0.9423103 |
| tbats | dy.qt | 2018-01-11 | 1440 | 0.0103775 | 0.0104334 | 1.4110712 | 1.1878852 |
| tbats | dy.qt | 2018-01-12 | 1440 | 0.0130046 | 0.0130904 | 2.1649021 | 1.4713606 |
| tbats | dy.qt | 2018-01-13 | 1 | 0.0147054 | 0.0148143 | 2.7456490 | 1.6570000 |
| tbats | dy.qt | 2018-01-15 | 1439 | 0.0177735 | 0.0179342 | 4.0444477 | 2.0110812 |
| tbats | dy.qt | 2018-01-16 | 1440 | 0.0175204 | 0.0176763 | 3.9235329 | 1.9807910 |
| tbats | dy.qt | 2018-01-17 | 1440 | 0.0173391 | 0.0174925 | 3.8604893 | 1.9648128 |
| tbats | dy.qt | 2018-01-18 | 1440 | 0.0132828 | 0.0133725 | 2.2636575 | 1.5045456 |
| tbats | dy.qt | 2018-01-19 | 1440 | 0.0169647 | 0.0171110 | 3.6821392 | 1.9188901 |
| tbats | dy.qt | 2018-01-20 | 1 | 0.0163738 | 0.0165090 | 3.4040250 | 1.8450000 |
| tbats | dy.qt | 2018-01-22 | 1439 | 0.0164475 | 0.0165846 | 3.4523110 | 1.8580396 |
| tbats | dy.qt | 2018-01-23 | 1440 | 0.0180156 | 0.0181820 | 4.1856644 | 2.0458896 |
| tbats | dy.qt | 2018-01-24 | 1440 | 0.0268881 | 0.0272614 | 9.3470521 | 3.0572949 |
| tbats | dy.qt | 2018-01-25 | 1440 | 0.0322722 | 0.0328036 | 13.2754630 | 3.6435509 |
| tbats | dy.qt | 2018-01-26 | 1440 | 0.0318377 | 0.0323591 | 13.0263583 | 3.6092047 |
| tbats | dy.qt | 2018-01-27 | 1 | 0.0359514 | 0.0366094 | 16.4106010 | 4.0510000 |
| tbats | dy.qt | 2018-01-29 | 1439 | 0.0339983 | 0.0345871 | 14.6966838 | 3.8336254 |
| tbats | dy.qt | 2018-01-30 | 1440 | 0.0346458 | 0.0352574 | 15.2604667 | 3.9064647 |
| tbats | dy.qt | 2018-01-31 | 1440 | 0.0333584 | 0.0339260 | 14.1707246 | 3.7644023 |
| tbats | dy.qt | 2018-02-01 | 1440 | 0.0288410 | 0.0292640 | 10.5843271 | 3.2533563 |
| tbats | dy.qt | 2018-02-02 | 1440 | 0.0249175 | 0.0252362 | 7.9895620 | 2.8265813 |
| tbats | dy.qt | 2018-02-03 | 1 | 0.0222400 | 0.0224901 | 6.2800360 | 2.5060000 |
| tbats | dy.qt | 2018-02-05 | 1439 | 0.0247250 | 0.0250364 | 7.8101566 | 2.7946657 |
| tbats | dy.qt | 2018-02-06 | 1440 | 0.0316136 | 0.0321241 | 12.7564999 | 3.5716243 |
| tbats | dy.qt | 2018-02-07 | 1440 | 0.0298147 | 0.0302673 | 11.3204578 | 3.3645888 |
| tbats | dy.qt | 2018-02-08 | 1440 | 0.0295570 | 0.0300045 | 11.1915858 | 3.3453828 |
| tbats | dy.qt | 2018-02-09 | 1440 | 0.0340752 | 0.0346683 | 14.8008132 | 3.8471825 |
| tbats | dy.qt | 2018-02-10 | 1 | 0.0344693 | 0.0350738 | 15.0854560 | 3.8840000 |
| tbats | dy.qt | 2018-02-12 | 1439 | 0.0355512 | 0.0361948 | 16.0525253 | 4.0065603 |
| tbats | dy.qt | 2018-02-13 | 1440 | 0.0415012 | 0.0423895 | 22.0797777 | 4.6989124 |
| tbats | dy.qt | 2018-02-14 | 1440 | 0.0478455 | 0.0490216 | 29.1477209 | 5.3988629 |
| tbats | dy.qt | 2018-02-15 | 1440 | 0.0548283 | 0.0563755 | 38.2107906 | 6.1814877 |
| tbats | dy.qt | 2018-02-16 | 1440 | 0.0585071 | 0.0602717 | 43.4960112 | 6.5951506 |
| tbats | dy.qt | 2018-02-17 | 1 | 0.0565673 | 0.0582138 | 40.6278760 | 6.3740000 |
| tbats | dy.qt | 2018-02-19 | 1439 | 0.0018810 | 0.0018789 | 0.0502889 | 0.2242519 |
| tbats | dy.qt | 2018-02-20 | 1440 | 0.0039150 | 0.0039051 | 0.2257944 | 0.4751782 |
| tbats | dy.qt | 2018-02-21 | 1440 | 0.0025510 | 0.0025468 | 0.0960670 | 0.3099467 |
| tbats | dy.qt | 2018-02-22 | 1440 | 0.0053739 | 0.0053927 | 0.4358929 | 0.6602219 |
| tbats | dy.qt | 2018-02-23 | 1440 | 0.0010663 | 0.0010658 | 0.0193807 | 0.1392147 |
| tbats | dy.qt | 2018-02-24 | 1 | 0.0012813 | 0.0012805 | 0.0187112 | 0.1367888 |
| tbats | dy.qt | 2018-02-26 | 1439 | 0.0017207 | 0.0017224 | 0.0487130 | 0.2207101 |
| tbats | dy.qt | 2018-02-27 | 1440 | 0.0017627 | 0.0017597 | 0.0692587 | 0.2631706 |
| tbats | dy.qt | 2018-02-28 | 1440 | 0.0028550 | 0.0028609 | 0.1383402 | 0.3719411 |
| tbats | dy.qt | 2018-03-01 | 1440 | 0.0014258 | 0.0014257 | 0.0407300 | 0.2018167 |
| tbats | dy.qt | 2018-03-02 | 1440 | 0.0044554 | 0.0044691 | 0.3069946 | 0.5540710 |
| tbats | dy.qt | 2018-03-03 | 1 | 0.0047471 | 0.0047584 | 0.2543040 | 0.5042856 |
| tbats | dy.qt | 2018-03-05 | 1439 | 0.0020813 | 0.0020805 | 0.0656674 | 0.2562565 |
| tbats | dy.qt | 2018-03-06 | 1440 | 0.0010507 | 0.0010510 | 0.0191561 | 0.1384056 |
| tbats | dy.qt | 2018-03-07 | 1440 | 0.0032845 | 0.0032912 | 0.1519726 | 0.3898366 |
| tbats | dy.qt | 2018-03-08 | 1440 | 0.0006005 | 0.0006004 | 0.0064385 | 0.0802403 |
| tbats | dy.qt | 2018-03-09 | 1440 | 0.0048093 | 0.0047965 | 0.2887926 | 0.5373943 |
| tbats | dy.qt | 2018-03-10 | 1 | 0.0057372 | 0.0057207 | 0.3713635 | 0.6093960 |
| tbats | dy.qt | 2018-03-12 | 1439 | 0.0023390 | 0.0023423 | 0.0759089 | 0.2755157 |
| tbats | dy.qt | 2018-03-13 | 1440 | 0.0028999 | 0.0028931 | 0.1572071 | 0.3964935 |
| tbats | dy.qt | 2018-03-14 | 1440 | 0.0013291 | 0.0013305 | 0.0331019 | 0.1819393 |
| tbats | dy.qt | 2018-03-15 | 1440 | 0.0023845 | 0.0023882 | 0.0828577 | 0.2878502 |
| tbats | dy.qt | 2018-03-16 | 1440 | 0.0033274 | 0.0033348 | 0.1665281 | 0.4080786 |
| tbats | dy.qt | 2018-03-17 | 1 | 0.0034003 | 0.0034061 | 0.1307541 | 0.3615994 |
| tbats | dy.qt | 2018-03-19 | 1439 | 0.0011850 | 0.0011852 | 0.0217987 | 0.1476438 |
| tbats | dy.qt | 2018-03-20 | 1440 | 0.0022856 | 0.0022823 | 0.0757474 | 0.2752225 |
| tbats | dy.qt | 2018-03-21 | 1440 | 0.0017213 | 0.0017237 | 0.0554248 | 0.2354247 |
| tbats | dy.qt | 2018-03-22 | 1440 | 0.0034462 | 0.0034537 | 0.1688976 | 0.4109715 |
| tbats | dy.qt | 2018-03-23 | 1440 | 0.0032304 | 0.0032366 | 0.1360697 | 0.3688763 |
| tbats | dy.qt | 2018-03-24 | 1 | 0.0051877 | 0.0052012 | 0.2983075 | 0.5461754 |
| tbats | dy.qt | 2018-03-26 | 1439 | 0.0028861 | 0.0028807 | 0.1198734 | 0.3462273 |
| tbats | dy.qt | 2018-03-27 | 1440 | 0.0019733 | 0.0019708 | 0.0548570 | 0.2342156 |
| tbats | dy.qt | 2018-03-28 | 1440 | 0.0054888 | 0.0054627 | 0.5830772 | 0.7635949 |
| tbats | dy.qt | 2018-03-29 | 1440 | 0.0026981 | 0.0027027 | 0.1069173 | 0.3269821 |
| tbats | dy.qt | 2018-03-30 | 1440 | 0.0017376 | 0.0017394 | 0.0399285 | 0.1998213 |
| tbats | dy.qt | 2018-03-31 | 1 | 0.0013576 | 0.0013585 | 0.0208770 | 0.1444887 |
| tbats | dy.qt | 2018-04-02 | 1439 | 0.0011295 | 0.0011310 | 0.0377658 | 0.1943343 |
| tbats | dy.qt | 2018-04-03 | 1440 | 0.0027903 | 0.0027837 | 0.1511955 | 0.3888386 |
| tbats | dy.qt | 2018-04-04 | 1440 | 0.0017291 | 0.0017314 | 0.0600898 | 0.2451322 |
| tbats | dy.qt | 2018-04-05 | 1440 | 0.0028588 | 0.0028526 | 0.1439445 | 0.3794002 |
| tbats | dy.qt | 2018-04-06 | 1440 | 0.0017676 | 0.0017703 | 0.0636784 | 0.2523457 |
| tbats | dy.qt | 2018-04-07 | 1 | 0.0041444 | 0.0041530 | 0.1980616 | 0.4450411 |
| tbats | dy.qt | 2018-04-09 | 1439 | 0.0009020 | 0.0009017 | 0.0139755 | 0.1182182 |
| tbats | dy.qt | 2018-04-10 | 1440 | 0.0024381 | 0.0024343 | 0.0871189 | 0.2951591 |
| tbats | dy.qt | 2018-04-11 | 1440 | 0.0020890 | 0.0020920 | 0.0689188 | 0.2625239 |
| tbats | dy.qt | 2018-04-12 | 1440 | 0.0022921 | 0.0022879 | 0.0981073 | 0.3132209 |
| tbats | dy.qt | 2018-04-13 | 1440 | 0.0015270 | 0.0015252 | 0.0423808 | 0.2058660 |
| tbats | dy.qt | 2018-04-14 | 1 | 0.0003289 | 0.0003289 | 0.0012460 | 0.0352982 |
| tbats | dy.qt | 2018-04-16 | 1439 | 0.0012836 | 0.0012842 | 0.0236461 | 0.1537730 |
| tbats | dy.qt | 2018-04-17 | 1440 | 0.0006967 | 0.0006970 | 0.0083520 | 0.0913892 |
| tbats | dy.qt | 2018-04-18 | 1440 | 0.0020366 | 0.0020342 | 0.0562271 | 0.2371224 |
| tbats | dy.qt | 2018-04-19 | 1440 | 0.0012621 | 0.0012611 | 0.0218887 | 0.1479484 |
| tbats | dy.qt | 2018-04-20 | 1440 | 0.0020490 | 0.0020465 | 0.0577120 | 0.2402333 |
| tbats | dy.qt | 2018-04-21 | 1 | 0.0025545 | 0.0025513 | 0.0752254 | 0.2742725 |
| tbats | dy.qt | 2018-04-23 | 1439 | 0.0045611 | 0.0045455 | 0.3645420 | 0.6037731 |
| tbats | dy.qt | 2018-04-24 | 1440 | 0.0011920 | 0.0011908 | 0.0309522 | 0.1759325 |
| tbats | dy.qt | 2018-04-25 | 1440 | 0.0027018 | 0.0026968 | 0.1197275 | 0.3460166 |
| tbats | dy.qt | 2018-04-26 | 1440 | 0.0010282 | 0.0010289 | 0.0189114 | 0.1375186 |
| tbats | dy.qt | 2018-04-27 | 1440 | 0.0008721 | 0.0008727 | 0.0162402 | 0.1274369 |
| tbats | dy.qt | 2018-04-28 | 1 | 0.0022253 | 0.0022278 | 0.0591608 | 0.2432299 |
| tbats | dy.qt | 2018-04-30 | 1439 | 0.0014960 | 0.0014945 | 0.0372243 | 0.1929359 |
| tbats | dy.qt | 2018-05-01 | 1440 | 0.0019179 | 0.0019150 | 0.0704245 | 0.2653761 |
| tbats | dy.qt | 2018-05-02 | 1440 | 0.0006541 | 0.0006544 | 0.0081468 | 0.0902595 |
| tbats | dy.qt | 2018-05-03 | 1440 | 0.0032235 | 0.0032314 | 0.1899514 | 0.4358341 |
| tbats | dy.qt | 2018-05-04 | 1440 | 0.0010354 | 0.0010363 | 0.0206722 | 0.1437784 |
| tbats | dy.qt | 2018-05-05 | 1 | 0.0010681 | 0.0010687 | 0.0136020 | 0.1166277 |
| tbats | dy.qt | 2018-05-07 | 1439 | 0.0010949 | 0.0010943 | 0.0214123 | 0.1463294 |
| tbats | dy.qt | 2018-05-08 | 1440 | 0.0008264 | 0.0008266 | 0.0120175 | 0.1096243 |
| tbats | dy.qt | 2018-05-09 | 1440 | 0.0041053 | 0.0040954 | 0.2378058 | 0.4876534 |
| tbats | dy.qt | 2018-05-10 | 1440 | 0.0013572 | 0.0013584 | 0.0376933 | 0.1941477 |
| tbats | dy.qt | 2018-05-11 | 1440 | 0.0007071 | 0.0007073 | 0.0085429 | 0.0924277 |
| tbats | dy.qt | 2018-05-12 | 1 | 0.0001085 | 0.0001085 | 0.0001408 | 0.0118658 |
| tbats | dy.qt | 2018-05-14 | 1439 | 0.0011015 | 0.0011008 | 0.0199788 | 0.1413464 |
| tbats | dy.qt | 2018-05-15 | 1440 | 0.0030341 | 0.0030269 | 0.1740472 | 0.4171897 |
| tbats | dy.qt | 2018-05-16 | 1440 | 0.0010763 | 0.0010771 | 0.0198791 | 0.1409933 |
| tbats | dy.qt | 2018-05-17 | 1440 | 0.0020281 | 0.0020259 | 0.0650995 | 0.2551460 |
| tbats | dy.qt | 2018-05-18 | 1440 | 0.0011063 | 0.0011057 | 0.0197986 | 0.1407074 |
| tbats | dy.qt | 2018-05-19 | 1 | 0.0001151 | 0.0001151 | 0.0001625 | 0.0127482 |
| tbats | dy.qt | 2018-05-21 | 1439 | 0.0034661 | 0.0034591 | 0.1709283 | 0.4134347 |
| tbats | dy.qt | 2018-05-22 | 1440 | 0.0008708 | 0.0008712 | 0.0117005 | 0.1081689 |
| tbats | dy.qt | 2018-05-23 | 1440 | 0.0057107 | 0.0057324 | 0.5328135 | 0.7299408 |
| tbats | dy.qt | 2018-05-24 | 1440 | 0.0049709 | 0.0049858 | 0.3584635 | 0.5987182 |
| tbats | dy.qt | 2018-05-25 | 1440 | 0.0016291 | 0.0016273 | 0.0430735 | 0.2075415 |
| tbats | dy.qt | 2018-05-26 | 1 | 0.0012189 | 0.0012181 | 0.0177330 | 0.1331653 |
| tbats | dy.qt | 2018-05-28 | 1439 | 0.0008189 | 0.0008182 | 0.0181025 | 0.1345455 |
| tbats | dy.qt | 2018-05-29 | 1440 | 0.0046705 | 0.0046848 | 0.3398971 | 0.5830070 |
| tbats | dy.qt | 2018-05-30 | 1440 | 0.0013349 | 0.0013351 | 0.0273525 | 0.1653860 |
| tbats | dy.qt | 2018-05-31 | 1440 | 0.0015381 | 0.0015397 | 0.0399489 | 0.1998722 |
| tbats | dy.qt | 2018-06-01 | 1440 | 0.0039078 | 0.0038975 | 0.2453799 | 0.4953583 |
| tbats | dy.qt | 2018-06-02 | 1 | 0.0064259 | 0.0064053 | 0.4889655 | 0.6992607 |
| tbats | dy.qt | 2018-06-04 | 1439 | 0.0009630 | 0.0009623 | 0.0173505 | 0.1317215 |
| tbats | dy.qt | 2018-06-05 | 1440 | 0.0006841 | 0.0006843 | 0.0091039 | 0.0954142 |
| tbats | dy.qt | 2018-06-06 | 1440 | 0.0020115 | 0.0020087 | 0.0660523 | 0.2570064 |
| tbats | dy.qt | 2018-06-07 | 1440 | 0.0020819 | 0.0020849 | 0.0739407 | 0.2719204 |
| tbats | dy.qt | 2018-06-08 | 1440 | 0.0016482 | 0.0016502 | 0.0492317 | 0.2218821 |
| tbats | dy.qt | 2018-06-09 | 1 | 0.0015419 | 0.0015431 | 0.0286111 | 0.1691482 |
| tbats | dy.qt | 2018-06-11 | 1439 | 0.0031046 | 0.0030989 | 0.1424658 | 0.3774465 |
| tbats | dy.qt | 2018-06-12 | 1440 | 0.0022461 | 0.0022432 | 0.0699830 | 0.2645429 |
| tbats | dy.qt | 2018-06-13 | 1440 | 0.0013507 | 0.0013493 | 0.0326393 | 0.1806636 |
| tbats | dy.qt | 2018-06-14 | 1440 | 0.0017004 | 0.0017015 | 0.0502469 | 0.2241582 |
| tbats | dy.qt | 2018-06-15 | 1440 | 0.0007257 | 0.0007257 | 0.0098517 | 0.0992559 |
| tbats | dy.qt | 2018-06-16 | 1 | 0.0003011 | 0.0003011 | 0.0011100 | 0.0333167 |
| tbats | dy.qt | 2018-06-18 | 1439 | 0.0014155 | 0.0014167 | 0.0292128 | 0.1709174 |
| tbats | dy.qt | 2018-06-19 | 1440 | 0.0052962 | 0.0053126 | 0.4011633 | 0.6333746 |
| tbats | dy.qt | 2018-06-20 | 1440 | 0.0009143 | 0.0009136 | 0.0188498 | 0.1372944 |
| tbats | dy.qt | 2018-06-21 | 1440 | 0.0019756 | 0.0019765 | 0.0688398 | 0.2623733 |
| tbats | dy.qt | 2018-06-22 | 1440 | 0.0006666 | 0.0006664 | 0.0087973 | 0.0937939 |
| tbats | dy.qt | 2018-06-23 | 1 | 0.0000166 | 0.0000166 | 0.0000034 | 0.0018304 |
| tbats | dy.qt | 2018-06-25 | 1439 | 0.0035492 | 0.0035565 | 0.1753105 | 0.4187009 |
| tbats | dy.qt | 2018-06-26 | 1440 | 0.0016580 | 0.0016579 | 0.0462228 | 0.2149950 |
| tbats | dy.qt | 2018-06-27 | 1440 | 0.0016472 | 0.0016466 | 0.0434048 | 0.2083381 |
| tbats | dy.qt | 2018-06-28 | 1440 | 0.0008681 | 0.0008678 | 0.0167567 | 0.1294476 |
| tbats | dy.qt | 2018-06-29 | 1440 | 0.0015291 | 0.0015275 | 0.0394970 | 0.1987385 |
| tbats | dy.qt | 2018-06-30 | 1 | 0.0017288 | 0.0017273 | 0.0364923 | 0.1910297 |
| tbats | dy.qt | 2018-07-02 | 1439 | 0.0010487 | 0.0010478 | 0.0211690 | 0.1454958 |
| tbats | dy.qt | 2018-07-03 | 1440 | 0.0012694 | 0.0012706 | 0.0347796 | 0.1864930 |
| tbats | dy.qt | 2018-07-04 | 1440 | 0.0010272 | 0.0010279 | 0.0163587 | 0.1279010 |
| tbats | dy.qt | 2018-07-05 | 1440 | 0.0009826 | 0.0009822 | 0.0142237 | 0.1192630 |
| tbats | dy.qt | 2018-07-06 | 1440 | 0.0008012 | 0.0008016 | 0.0131406 | 0.1146326 |
| tbats | dy.qt | 2018-07-07 | 1 | 0.0016441 | 0.0016454 | 0.0330902 | 0.1819072 |
| tbats | dy.wk | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.wk | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.wk | 2018-01-05 | 1440 | 0.0033088 | 0.0033021 | 0.1710646 | 0.4135996 |
| tbats | dy.wk | 2018-01-06 | 1 | 0.0033875 | 0.0033818 | 0.1456973 | 0.3817032 |
| tbats | dy.wk | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050746 | 0.4528517 |
| tbats | dy.wk | 2018-01-09 | 1440 | 0.0033033 | 0.0033099 | 0.1699884 | 0.4122964 |
| tbats | dy.wk | 2018-01-10 | 1440 | 0.0070823 | 0.0071157 | 0.8429946 | 0.9181474 |
| tbats | dy.wk | 2018-01-11 | 1440 | 0.0016816 | 0.0016808 | 0.0501580 | 0.2239599 |
| tbats | dy.wk | 2018-01-12 | 1440 | 0.0009501 | 0.0009504 | 0.0195186 | 0.1397089 |
| tbats | dy.wk | 2018-01-13 | 1 | 0.0021095 | 0.0021117 | 0.0550810 | 0.2346935 |
| tbats | dy.wk | 2018-01-15 | 1439 | 0.0032362 | 0.0032424 | 0.1531030 | 0.3912838 |
| tbats | dy.wk | 2018-01-16 | 1440 | 0.0018544 | 0.0018525 | 0.0536890 | 0.2317088 |
| tbats | dy.wk | 2018-01-17 | 1440 | 0.0026475 | 0.0026428 | 0.1169025 | 0.3419100 |
| tbats | dy.wk | 2018-01-18 | 1440 | 0.0012101 | 0.0012114 | 0.0359619 | 0.1896363 |
| tbats | dy.wk | 2018-01-19 | 1440 | 0.0030660 | 0.0030718 | 0.1439751 | 0.3794405 |
| tbats | dy.wk | 2018-01-20 | 1 | 0.0024655 | 0.0024686 | 0.0750436 | 0.2739409 |
| tbats | dy.wk | 2018-01-22 | 1439 | 0.0009873 | 0.0009876 | 0.0163756 | 0.1279671 |
| tbats | dy.wk | 2018-01-23 | 1440 | 0.0027142 | 0.0027197 | 0.1398581 | 0.3739761 |
| tbats | dy.wk | 2018-01-24 | 1440 | 0.0059675 | 0.0059923 | 0.6004194 | 0.7748674 |
| tbats | dy.wk | 2018-01-25 | 1440 | 0.0021126 | 0.0021156 | 0.0835002 | 0.2889640 |
| tbats | dy.wk | 2018-01-26 | 1440 | 0.0035816 | 0.0035920 | 0.2611903 | 0.5110678 |
| tbats | dy.wk | 2018-01-27 | 1 | 0.0071941 | 0.0072201 | 0.6196136 | 0.7871554 |
| tbats | dy.wk | 2018-01-29 | 1439 | 0.0020564 | 0.0020535 | 0.0690647 | 0.2628016 |
| tbats | dy.wk | 2018-01-30 | 1440 | 0.0017874 | 0.0017895 | 0.0517931 | 0.2275810 |
| tbats | dy.wk | 2018-01-31 | 1440 | 0.0015934 | 0.0015909 | 0.0616313 | 0.2482566 |
| tbats | dy.wk | 2018-02-01 | 1440 | 0.0011203 | 0.0011196 | 0.0247870 | 0.1574389 |
| tbats | dy.wk | 2018-02-02 | 1440 | 0.0048623 | 0.0048453 | 0.4069810 | 0.6379507 |
| tbats | dy.wk | 2018-02-03 | 1 | 0.0081074 | 0.0080746 | 0.7850625 | 0.8860375 |
| tbats | dy.wk | 2018-02-05 | 1439 | 0.0026205 | 0.0026257 | 0.1271709 | 0.3566103 |
| tbats | dy.wk | 2018-02-06 | 1440 | 0.0037161 | 0.0037067 | 0.2334475 | 0.4831641 |
| tbats | dy.wk | 2018-02-07 | 1440 | 0.0023571 | 0.0023609 | 0.0938273 | 0.3063124 |
| tbats | dy.wk | 2018-02-08 | 1440 | 0.0024018 | 0.0024023 | 0.1001020 | 0.3163889 |
| tbats | dy.wk | 2018-02-09 | 1440 | 0.0019856 | 0.0019845 | 0.0676120 | 0.2600231 |
| tbats | dy.wk | 2018-02-10 | 1 | 0.0004671 | 0.0004670 | 0.0025805 | 0.0507983 |
| tbats | dy.wk | 2018-02-12 | 1439 | 0.0011769 | 0.0011777 | 0.0201046 | 0.1417906 |
| tbats | dy.wk | 2018-02-13 | 1440 | 0.0061915 | 0.0062186 | 0.6394205 | 0.7996377 |
| tbats | dy.wk | 2018-02-14 | 1440 | 0.0049932 | 0.0050093 | 0.3709035 | 0.6090185 |
| tbats | dy.wk | 2018-02-15 | 1440 | 0.0047575 | 0.0047707 | 0.3015634 | 0.5491478 |
| tbats | dy.wk | 2018-02-16 | 1440 | 0.0013685 | 0.0013695 | 0.0367192 | 0.1916226 |
| tbats | dy.wk | 2018-02-17 | 1 | 0.0016104 | 0.0016091 | 0.0292141 | 0.1709213 |
| tbats | dy.wk | 2018-02-19 | 1439 | 0.0018805 | 0.0018784 | 0.0502621 | 0.2241921 |
| tbats | dy.wk | 2018-02-20 | 1440 | 0.0039150 | 0.0039051 | 0.2257968 | 0.4751808 |
| tbats | dy.wk | 2018-02-21 | 1440 | 0.0025499 | 0.0025457 | 0.0959955 | 0.3098313 |
| tbats | dy.wk | 2018-02-22 | 1440 | 0.0053737 | 0.0053926 | 0.4358756 | 0.6602088 |
| tbats | dy.wk | 2018-02-23 | 1440 | 0.0010670 | 0.0010664 | 0.0194055 | 0.1393037 |
| tbats | dy.wk | 2018-02-24 | 1 | 0.0012833 | 0.0012825 | 0.0187688 | 0.1369993 |
| tbats | dy.wk | 2018-02-26 | 1439 | 0.0017220 | 0.0017237 | 0.0488638 | 0.2210515 |
| tbats | dy.wk | 2018-02-27 | 1440 | 0.0017673 | 0.0017643 | 0.0695155 | 0.2636579 |
| tbats | dy.wk | 2018-02-28 | 1440 | 0.0028541 | 0.0028600 | 0.1382644 | 0.3718393 |
| tbats | dy.wk | 2018-03-01 | 1440 | 0.0034801 | 0.0034715 | 0.1949716 | 0.4415559 |
| tbats | dy.wk | 2018-03-02 | 1440 | 0.0044533 | 0.0044669 | 0.3068255 | 0.5539184 |
| tbats | dy.wk | 2018-03-03 | 1 | 0.0047465 | 0.0047578 | 0.2542418 | 0.5042239 |
| tbats | dy.wk | 2018-03-05 | 1439 | 0.0020804 | 0.0020796 | 0.0656607 | 0.2562435 |
| tbats | dy.wk | 2018-03-06 | 1440 | 0.0010509 | 0.0010512 | 0.0191605 | 0.1384215 |
| tbats | dy.wk | 2018-03-07 | 1440 | 0.0032838 | 0.0032906 | 0.1519181 | 0.3897667 |
| tbats | dy.wk | 2018-03-08 | 1440 | 0.0006008 | 0.0006007 | 0.0064412 | 0.0802573 |
| tbats | dy.wk | 2018-03-09 | 1440 | 0.0048046 | 0.0047919 | 0.2882737 | 0.5369113 |
| tbats | dy.wk | 2018-03-10 | 1 | 0.0057323 | 0.0057160 | 0.3707431 | 0.6088868 |
| tbats | dy.wk | 2018-03-12 | 1439 | 0.0023320 | 0.0023352 | 0.0754334 | 0.2746514 |
| tbats | dy.wk | 2018-03-13 | 1440 | 0.0028998 | 0.0028929 | 0.1571936 | 0.3964765 |
| tbats | dy.wk | 2018-03-14 | 1440 | 0.0013293 | 0.0013307 | 0.0331099 | 0.1819613 |
| tbats | dy.wk | 2018-03-15 | 1440 | 0.0023848 | 0.0023884 | 0.0828737 | 0.2878779 |
| tbats | dy.wk | 2018-03-16 | 1440 | 0.0033265 | 0.0033339 | 0.1664579 | 0.4079926 |
| tbats | dy.wk | 2018-03-17 | 1 | 0.0033993 | 0.0034051 | 0.1306823 | 0.3615001 |
| tbats | dy.wk | 2018-03-19 | 1439 | 0.0011853 | 0.0011856 | 0.0218139 | 0.1476954 |
| tbats | dy.wk | 2018-03-20 | 1440 | 0.0022842 | 0.0022809 | 0.0756495 | 0.2750445 |
| tbats | dy.wk | 2018-03-21 | 1440 | 0.0017213 | 0.0017238 | 0.0554276 | 0.2354307 |
| tbats | dy.wk | 2018-03-22 | 1440 | 0.0034475 | 0.0034551 | 0.1690138 | 0.4111129 |
| tbats | dy.wk | 2018-03-23 | 1440 | 0.0032325 | 0.0032386 | 0.1362323 | 0.3690966 |
| tbats | dy.wk | 2018-03-24 | 1 | 0.0051900 | 0.0052035 | 0.2985701 | 0.5464157 |
| tbats | dy.wk | 2018-03-26 | 1439 | 0.0028768 | 0.0028713 | 0.1192208 | 0.3452836 |
| tbats | dy.wk | 2018-03-27 | 1440 | 0.0019802 | 0.0019777 | 0.0551823 | 0.2349091 |
| tbats | dy.wk | 2018-03-28 | 1440 | 0.0054936 | 0.0054675 | 0.5836692 | 0.7639825 |
| tbats | dy.wk | 2018-03-29 | 1440 | 0.0026980 | 0.0027026 | 0.1069109 | 0.3269724 |
| tbats | dy.wk | 2018-03-30 | 1440 | 0.0017345 | 0.0017362 | 0.0397680 | 0.1994193 |
| tbats | dy.wk | 2018-03-31 | 1 | 0.0013532 | 0.0013541 | 0.0207413 | 0.1440184 |
| tbats | dy.wk | 2018-04-02 | 1439 | 0.0011295 | 0.0011310 | 0.0377658 | 0.1943343 |
| tbats | dy.wk | 2018-04-03 | 1440 | 0.0027909 | 0.0027843 | 0.1512560 | 0.3889164 |
| tbats | dy.wk | 2018-04-04 | 1440 | 0.0045689 | 0.0045824 | 0.3085447 | 0.5554680 |
| tbats | dy.wk | 2018-04-05 | 1440 | 0.0028622 | 0.0028559 | 0.1442011 | 0.3797382 |
| tbats | dy.wk | 2018-04-06 | 1440 | 0.0041438 | 0.0041560 | 0.2821475 | 0.5311755 |
| tbats | dy.wk | 2018-04-07 | 1 | 0.0090231 | 0.0090640 | 0.9480926 | 0.9737005 |
| tbats | dy.wk | 2018-04-09 | 1439 | 0.0009029 | 0.0009026 | 0.0139964 | 0.1183064 |
| tbats | dy.wk | 2018-04-10 | 1440 | 0.0026414 | 0.0026370 | 0.1022641 | 0.3197875 |
| tbats | dy.wk | 2018-04-11 | 1440 | 0.0020889 | 0.0020919 | 0.0689249 | 0.2625356 |
| tbats | dy.wk | 2018-04-12 | 1440 | 0.0022912 | 0.0022869 | 0.0980558 | 0.3131386 |
| tbats | dy.wk | 2018-04-13 | 1440 | 0.0015215 | 0.0015197 | 0.0421439 | 0.2052899 |
| tbats | dy.wk | 2018-04-14 | 1 | 0.0003216 | 0.0003215 | 0.0011913 | 0.0345146 |
| tbats | dy.wk | 2018-04-16 | 1439 | 0.0012819 | 0.0012826 | 0.0235916 | 0.1535956 |
| tbats | dy.wk | 2018-04-17 | 1440 | 0.0011470 | 0.0011479 | 0.0198544 | 0.1409056 |
| tbats | dy.wk | 2018-04-18 | 1440 | 0.0020339 | 0.0020315 | 0.0560938 | 0.2368412 |
| tbats | dy.wk | 2018-04-19 | 1440 | 0.0012757 | 0.0012747 | 0.0223559 | 0.1495189 |
| tbats | dy.wk | 2018-04-20 | 1440 | 0.0020583 | 0.0020558 | 0.0581683 | 0.2411810 |
| tbats | dy.wk | 2018-04-21 | 1 | 0.0025642 | 0.0025609 | 0.0757940 | 0.2753071 |
| tbats | dy.wk | 2018-04-23 | 1439 | 0.0045527 | 0.0045371 | 0.3635059 | 0.6029145 |
| tbats | dy.wk | 2018-04-24 | 1440 | 0.0025250 | 0.0025303 | 0.1285007 | 0.3584699 |
| tbats | dy.wk | 2018-04-25 | 1440 | 0.0027056 | 0.0027005 | 0.1200492 | 0.3464812 |
| tbats | dy.wk | 2018-04-26 | 1440 | 0.0010286 | 0.0010293 | 0.0189224 | 0.1375586 |
| tbats | dy.wk | 2018-04-27 | 1440 | 0.0013823 | 0.0013840 | 0.0406709 | 0.2016704 |
| tbats | dy.wk | 2018-04-28 | 1 | 0.0036471 | 0.0036538 | 0.1593622 | 0.3992019 |
| tbats | dy.wk | 2018-04-30 | 1439 | 0.0014982 | 0.0014966 | 0.0373042 | 0.1931430 |
| tbats | dy.wk | 2018-05-01 | 1440 | 0.0019000 | 0.0018972 | 0.0692574 | 0.2631681 |
| tbats | dy.wk | 2018-05-02 | 1440 | 0.0028107 | 0.0028155 | 0.1187572 | 0.3446116 |
| tbats | dy.wk | 2018-05-03 | 1440 | 0.0032648 | 0.0032729 | 0.1935239 | 0.4399135 |
| tbats | dy.wk | 2018-05-04 | 1440 | 0.0010356 | 0.0010365 | 0.0206815 | 0.1438108 |
| tbats | dy.wk | 2018-05-05 | 1 | 0.0010683 | 0.0010689 | 0.0136074 | 0.1166506 |
| tbats | dy.wk | 2018-05-07 | 1439 | 0.0010945 | 0.0010939 | 0.0213986 | 0.1462826 |
| tbats | dy.wk | 2018-05-08 | 1440 | 0.0008267 | 0.0008270 | 0.0120254 | 0.1096602 |
| tbats | dy.wk | 2018-05-09 | 1440 | 0.0041100 | 0.0041001 | 0.2384303 | 0.4882932 |
| tbats | dy.wk | 2018-05-10 | 1440 | 0.0013582 | 0.0013594 | 0.0377419 | 0.1942729 |
| tbats | dy.wk | 2018-05-11 | 1440 | 0.0007075 | 0.0007077 | 0.0085526 | 0.0924805 |
| tbats | dy.wk | 2018-05-12 | 1 | 0.0001094 | 0.0001094 | 0.0001433 | 0.0119728 |
| tbats | dy.wk | 2018-05-14 | 1439 | 0.0011874 | 0.0011865 | 0.0241623 | 0.1554422 |
| tbats | dy.wk | 2018-05-15 | 1440 | 0.0030442 | 0.0030370 | 0.1747856 | 0.4180737 |
| tbats | dy.wk | 2018-05-16 | 1440 | 0.0010725 | 0.0010733 | 0.0197762 | 0.1406280 |
| tbats | dy.wk | 2018-05-17 | 1440 | 0.0020402 | 0.0020379 | 0.0666682 | 0.2582019 |
| tbats | dy.wk | 2018-05-18 | 1440 | 0.0011086 | 0.0011080 | 0.0198944 | 0.1410475 |
| tbats | dy.wk | 2018-05-19 | 1 | 0.0001102 | 0.0001102 | 0.0001489 | 0.0122034 |
| tbats | dy.wk | 2018-05-21 | 1439 | 0.0034650 | 0.0034581 | 0.1708403 | 0.4133283 |
| tbats | dy.wk | 2018-05-22 | 1440 | 0.0008503 | 0.0008507 | 0.0112249 | 0.1059478 |
| tbats | dy.wk | 2018-05-23 | 1440 | 0.0057203 | 0.0057421 | 0.5342530 | 0.7309261 |
| tbats | dy.wk | 2018-05-24 | 1440 | 0.0049609 | 0.0049757 | 0.3572356 | 0.5976919 |
| tbats | dy.wk | 2018-05-25 | 1440 | 0.0016314 | 0.0016297 | 0.0431855 | 0.2078112 |
| tbats | dy.wk | 2018-05-26 | 1 | 0.0012219 | 0.0012212 | 0.0178230 | 0.1335029 |
| tbats | dy.wk | 2018-05-28 | 1439 | 0.0008202 | 0.0008195 | 0.0181591 | 0.1347557 |
| tbats | dy.wk | 2018-05-29 | 1440 | 0.0046705 | 0.0046847 | 0.3398943 | 0.5830045 |
| tbats | dy.wk | 2018-05-30 | 1440 | 0.0013343 | 0.0013346 | 0.0274149 | 0.1655744 |
| tbats | dy.wk | 2018-05-31 | 1440 | 0.0015399 | 0.0015416 | 0.0400234 | 0.2000586 |
| tbats | dy.wk | 2018-06-01 | 1440 | 0.0039110 | 0.0039006 | 0.2457697 | 0.4957517 |
| tbats | dy.wk | 2018-06-02 | 1 | 0.0064302 | 0.0064096 | 0.4896202 | 0.6997287 |
| tbats | dy.wk | 2018-06-04 | 1439 | 0.0009617 | 0.0009610 | 0.0173077 | 0.1315586 |
| tbats | dy.wk | 2018-06-05 | 1440 | 0.0006840 | 0.0006841 | 0.0090982 | 0.0953846 |
| tbats | dy.wk | 2018-06-06 | 1440 | 0.0020146 | 0.0020119 | 0.0662048 | 0.2573030 |
| tbats | dy.wk | 2018-06-07 | 1440 | 0.0020963 | 0.0020993 | 0.0746822 | 0.2732804 |
| tbats | dy.wk | 2018-06-08 | 1440 | 0.0016456 | 0.0016476 | 0.0490690 | 0.2215153 |
| tbats | dy.wk | 2018-06-09 | 1 | 0.0015372 | 0.0015384 | 0.0284363 | 0.1686308 |
| tbats | dy.wk | 2018-06-11 | 1439 | 0.0031315 | 0.0031257 | 0.1457279 | 0.3817432 |
| tbats | dy.wk | 2018-06-12 | 1440 | 0.0022426 | 0.0022397 | 0.0697875 | 0.2641732 |
| tbats | dy.wk | 2018-06-13 | 1440 | 0.0013509 | 0.0013496 | 0.0326473 | 0.1806855 |
| tbats | dy.wk | 2018-06-14 | 1440 | 0.0017764 | 0.0017755 | 0.0582218 | 0.2412920 |
| tbats | dy.wk | 2018-06-15 | 1440 | 0.0007286 | 0.0007286 | 0.0099876 | 0.0999379 |
| tbats | dy.wk | 2018-06-16 | 1 | 0.0002951 | 0.0002950 | 0.0010657 | 0.0326457 |
| tbats | dy.wk | 2018-06-18 | 1439 | 0.0026771 | 0.0026812 | 0.1024901 | 0.3201407 |
| tbats | dy.wk | 2018-06-19 | 1440 | 0.0049596 | 0.0049741 | 0.3531118 | 0.5942321 |
| tbats | dy.wk | 2018-06-20 | 1440 | 0.0009217 | 0.0009210 | 0.0190658 | 0.1380790 |
| tbats | dy.wk | 2018-06-21 | 1440 | 0.0019756 | 0.0019765 | 0.0688409 | 0.2623755 |
| tbats | dy.wk | 2018-06-22 | 1440 | 0.0006667 | 0.0006665 | 0.0087705 | 0.0936508 |
| tbats | dy.wk | 2018-06-23 | 1 | 0.0000121 | 0.0000121 | 0.0000018 | 0.0013278 |
| tbats | dy.wk | 2018-06-25 | 1439 | 0.0035498 | 0.0035570 | 0.1753596 | 0.4187597 |
| tbats | dy.wk | 2018-06-26 | 1440 | 0.0016588 | 0.0016587 | 0.0462352 | 0.2150238 |
| tbats | dy.wk | 2018-06-27 | 1440 | 0.0016475 | 0.0016468 | 0.0434671 | 0.2084877 |
| tbats | dy.wk | 2018-06-28 | 1440 | 0.0008682 | 0.0008679 | 0.0167661 | 0.1294839 |
| tbats | dy.wk | 2018-06-29 | 1440 | 0.0015295 | 0.0015279 | 0.0395188 | 0.1987934 |
| tbats | dy.wk | 2018-06-30 | 1 | 0.0017294 | 0.0017280 | 0.0365186 | 0.1910984 |
| tbats | dy.wk | 2018-07-02 | 1439 | 0.0010502 | 0.0010493 | 0.0212118 | 0.1456428 |
| tbats | dy.wk | 2018-07-03 | 1440 | 0.0012720 | 0.0012733 | 0.0349115 | 0.1868461 |
| tbats | dy.wk | 2018-07-04 | 1440 | 0.0010274 | 0.0010281 | 0.0163644 | 0.1279235 |
| tbats | dy.wk | 2018-07-05 | 1440 | 0.0009804 | 0.0009800 | 0.0141518 | 0.1189613 |
| tbats | dy.wk | 2018-07-06 | 1440 | 0.0012390 | 0.0012403 | 0.0328218 | 0.1811678 |
| tbats | dy.wk | 2018-07-07 | 1 | 0.0028486 | 0.0028526 | 0.0995788 | 0.3155610 |
| tbats | dy.wk.mo | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.wk.mo | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.wk.mo | 2018-01-05 | 1440 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| tbats | dy.wk.mo | 2018-01-06 | 1 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| tbats | dy.wk.mo | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050746 | 0.4528517 |
| tbats | dy.wk.mo | 2018-01-09 | 1440 | 0.0012943 | 0.0012931 | 0.0419181 | 0.2047390 |
| tbats | dy.wk.mo | 2018-01-10 | 1440 | 0.0073048 | 0.0073400 | 0.8879488 | 0.9423103 |
| tbats | dy.wk.mo | 2018-01-11 | 1440 | 0.0103775 | 0.0104334 | 1.4110712 | 1.1878852 |
| tbats | dy.wk.mo | 2018-01-12 | 1440 | 0.0130046 | 0.0130904 | 2.1649021 | 1.4713606 |
| tbats | dy.wk.mo | 2018-01-13 | 1 | 0.0147054 | 0.0148143 | 2.7456490 | 1.6570000 |
| tbats | dy.wk.mo | 2018-01-15 | 1439 | 0.0177735 | 0.0179342 | 4.0444477 | 2.0110812 |
| tbats | dy.wk.mo | 2018-01-16 | 1440 | 0.0175204 | 0.0176763 | 3.9235329 | 1.9807910 |
| tbats | dy.wk.mo | 2018-01-17 | 1440 | 0.0173391 | 0.0174925 | 3.8604893 | 1.9648128 |
| tbats | dy.wk.mo | 2018-01-18 | 1440 | 0.0132828 | 0.0133725 | 2.2636575 | 1.5045456 |
| tbats | dy.wk.mo | 2018-01-19 | 1440 | 0.0030752 | 0.0030811 | 0.1457174 | 0.3817295 |
| tbats | dy.wk.mo | 2018-01-20 | 1 | 0.0024662 | 0.0024692 | 0.0750853 | 0.2740170 |
| tbats | dy.wk.mo | 2018-01-22 | 1439 | 0.0009303 | 0.0009302 | 0.0176595 | 0.1328892 |
| tbats | dy.wk.mo | 2018-01-23 | 1440 | 0.0027046 | 0.0027101 | 0.1387591 | 0.3725038 |
| tbats | dy.wk.mo | 2018-01-24 | 1440 | 0.0059686 | 0.0059934 | 0.6005825 | 0.7749726 |
| tbats | dy.wk.mo | 2018-01-25 | 1440 | 0.0021473 | 0.0021505 | 0.0859467 | 0.2931666 |
| tbats | dy.wk.mo | 2018-01-26 | 1440 | 0.0035812 | 0.0035916 | 0.2611411 | 0.5110197 |
| tbats | dy.wk.mo | 2018-01-27 | 1 | 0.0071935 | 0.0072194 | 0.6194986 | 0.7870823 |
| tbats | dy.wk.mo | 2018-01-29 | 1439 | 0.0020564 | 0.0020535 | 0.0690656 | 0.2628034 |
| tbats | dy.wk.mo | 2018-01-30 | 1440 | 0.0017877 | 0.0017898 | 0.0518050 | 0.2276070 |
| tbats | dy.wk.mo | 2018-01-31 | 1440 | 0.0015933 | 0.0015908 | 0.0616274 | 0.2482488 |
| tbats | dy.wk.mo | 2018-02-01 | 1440 | 0.0021337 | 0.0021305 | 0.0759029 | 0.2755049 |
| tbats | dy.wk.mo | 2018-02-02 | 1440 | 0.0043713 | 0.0043575 | 0.3328524 | 0.5769336 |
| tbats | dy.wk.mo | 2018-02-03 | 1 | 0.0071076 | 0.0070825 | 0.6045852 | 0.7775508 |
| tbats | dy.wk.mo | 2018-02-05 | 1439 | 0.0026140 | 0.0026193 | 0.1267198 | 0.3559773 |
| tbats | dy.wk.mo | 2018-02-06 | 1440 | 0.0019389 | 0.0019386 | 0.0696284 | 0.2638719 |
| tbats | dy.wk.mo | 2018-02-07 | 1440 | 0.0023370 | 0.0023408 | 0.0920691 | 0.3034290 |
| tbats | dy.wk.mo | 2018-02-08 | 1440 | 0.0024023 | 0.0024028 | 0.1001123 | 0.3164052 |
| tbats | dy.wk.mo | 2018-02-09 | 1440 | 0.0019902 | 0.0019891 | 0.0678287 | 0.2604395 |
| tbats | dy.wk.mo | 2018-02-10 | 1 | 0.0004776 | 0.0004774 | 0.0026968 | 0.0519307 |
| tbats | dy.wk.mo | 2018-02-12 | 1439 | 0.0011760 | 0.0011769 | 0.0200777 | 0.1416960 |
| tbats | dy.wk.mo | 2018-02-13 | 1440 | 0.0061903 | 0.0062174 | 0.6391231 | 0.7994518 |
| tbats | dy.wk.mo | 2018-02-14 | 1440 | 0.0049948 | 0.0050108 | 0.3710984 | 0.6091785 |
| tbats | dy.wk.mo | 2018-02-15 | 1440 | 0.0047574 | 0.0047706 | 0.3015522 | 0.5491377 |
| tbats | dy.wk.mo | 2018-02-16 | 1440 | 0.0013685 | 0.0013696 | 0.0367487 | 0.1916994 |
| tbats | dy.wk.mo | 2018-02-17 | 1 | 0.0016075 | 0.0016062 | 0.0291089 | 0.1706133 |
| tbats | dy.wk.mo | 2018-02-19 | 1439 | 0.0018805 | 0.0018784 | 0.0502614 | 0.2241906 |
| tbats | dy.wk.mo | 2018-02-20 | 1440 | 0.0039149 | 0.0039050 | 0.2257887 | 0.4751723 |
| tbats | dy.wk.mo | 2018-02-21 | 1440 | 0.0025511 | 0.0025469 | 0.0960761 | 0.3099615 |
| tbats | dy.wk.mo | 2018-02-22 | 1440 | 0.0053754 | 0.0053942 | 0.4360783 | 0.6603622 |
| tbats | dy.wk.mo | 2018-02-23 | 1440 | 0.0010670 | 0.0010665 | 0.0194061 | 0.1393059 |
| tbats | dy.wk.mo | 2018-02-24 | 1 | 0.0012833 | 0.0012825 | 0.0187697 | 0.1370025 |
| tbats | dy.wk.mo | 2018-02-26 | 1439 | 0.0017210 | 0.0017227 | 0.0487486 | 0.2207908 |
| tbats | dy.wk.mo | 2018-02-27 | 1440 | 0.0017591 | 0.0017561 | 0.0690596 | 0.2627920 |
| tbats | dy.wk.mo | 2018-02-28 | 1440 | 0.0028549 | 0.0028608 | 0.1383295 | 0.3719268 |
| tbats | dy.wk.mo | 2018-03-01 | 1440 | 0.0014257 | 0.0014256 | 0.0407275 | 0.2018106 |
| tbats | dy.wk.mo | 2018-03-02 | 1440 | 0.0044566 | 0.0044703 | 0.3071276 | 0.5541909 |
| tbats | dy.wk.mo | 2018-03-03 | 1 | 0.0047484 | 0.0047597 | 0.2544465 | 0.5044269 |
| tbats | dy.wk.mo | 2018-03-05 | 1439 | 0.0020815 | 0.0020807 | 0.0656695 | 0.2562606 |
| tbats | dy.wk.mo | 2018-03-06 | 1440 | 0.0010504 | 0.0010507 | 0.0191440 | 0.1383618 |
| tbats | dy.wk.mo | 2018-03-07 | 1440 | 0.0032837 | 0.0032905 | 0.1519105 | 0.3897570 |
| tbats | dy.wk.mo | 2018-03-08 | 1440 | 0.0006008 | 0.0006007 | 0.0064422 | 0.0802634 |
| tbats | dy.wk.mo | 2018-03-09 | 1440 | 0.0048029 | 0.0047901 | 0.2880749 | 0.5367261 |
| tbats | dy.wk.mo | 2018-03-10 | 1 | 0.0057305 | 0.0057141 | 0.3705054 | 0.6086915 |
| tbats | dy.wk.mo | 2018-03-12 | 1439 | 0.0023398 | 0.0023430 | 0.0759610 | 0.2756103 |
| tbats | dy.wk.mo | 2018-03-13 | 1440 | 0.0028991 | 0.0028923 | 0.1571326 | 0.3963996 |
| tbats | dy.wk.mo | 2018-03-14 | 1440 | 0.0011253 | 0.0011263 | 0.0244596 | 0.1563956 |
| tbats | dy.wk.mo | 2018-03-15 | 1440 | 0.0023833 | 0.0023870 | 0.0827863 | 0.2877261 |
| tbats | dy.wk.mo | 2018-03-16 | 1440 | 0.0033265 | 0.0033339 | 0.1664580 | 0.4079926 |
| tbats | dy.wk.mo | 2018-03-17 | 1 | 0.0033993 | 0.0034051 | 0.1306824 | 0.3615002 |
| tbats | dy.wk.mo | 2018-03-19 | 1439 | 0.0011848 | 0.0011850 | 0.0217902 | 0.1476152 |
| tbats | dy.wk.mo | 2018-03-20 | 1440 | 0.0022841 | 0.0022809 | 0.0756456 | 0.2750375 |
| tbats | dy.wk.mo | 2018-03-21 | 1440 | 0.0017210 | 0.0017235 | 0.0554153 | 0.2354047 |
| tbats | dy.wk.mo | 2018-03-22 | 1440 | 0.0034394 | 0.0034469 | 0.1683285 | 0.4102786 |
| tbats | dy.wk.mo | 2018-03-23 | 1440 | 0.0032312 | 0.0032373 | 0.1361282 | 0.3689556 |
| tbats | dy.wk.mo | 2018-03-24 | 1 | 0.0051886 | 0.0052021 | 0.2984034 | 0.5462631 |
| tbats | dy.wk.mo | 2018-03-26 | 1439 | 0.0028815 | 0.0028761 | 0.1195559 | 0.3457686 |
| tbats | dy.wk.mo | 2018-03-27 | 1440 | 0.0019748 | 0.0019723 | 0.0549293 | 0.2343699 |
| tbats | dy.wk.mo | 2018-03-28 | 1440 | 0.0054901 | 0.0054639 | 0.5832300 | 0.7636949 |
| tbats | dy.wk.mo | 2018-03-29 | 1440 | 0.0026988 | 0.0027033 | 0.1069614 | 0.3270495 |
| tbats | dy.wk.mo | 2018-03-30 | 1440 | 0.0017393 | 0.0017410 | 0.0400147 | 0.2000367 |
| tbats | dy.wk.mo | 2018-03-31 | 1 | 0.0013599 | 0.0013609 | 0.0209498 | 0.1447405 |
| tbats | dy.wk.mo | 2018-04-02 | 1439 | 0.0011293 | 0.0011308 | 0.0377876 | 0.1943902 |
| tbats | dy.wk.mo | 2018-04-03 | 1440 | 0.0027846 | 0.0027780 | 0.1506152 | 0.3880917 |
| tbats | dy.wk.mo | 2018-04-04 | 1440 | 0.0017290 | 0.0017314 | 0.0600872 | 0.2451269 |
| tbats | dy.wk.mo | 2018-04-05 | 1440 | 0.0028603 | 0.0028540 | 0.1440676 | 0.3795623 |
| tbats | dy.wk.mo | 2018-04-06 | 1440 | 0.0017683 | 0.0017710 | 0.0637238 | 0.2524357 |
| tbats | dy.wk.mo | 2018-04-07 | 1 | 0.0041456 | 0.0041542 | 0.1981732 | 0.4451665 |
| tbats | dy.wk.mo | 2018-04-09 | 1439 | 0.0009015 | 0.0009013 | 0.0139655 | 0.1181757 |
| tbats | dy.wk.mo | 2018-04-10 | 1440 | 0.0026385 | 0.0026340 | 0.1020143 | 0.3193967 |
| tbats | dy.wk.mo | 2018-04-11 | 1440 | 0.0020930 | 0.0020960 | 0.0691462 | 0.2629567 |
| tbats | dy.wk.mo | 2018-04-12 | 1440 | 0.0022877 | 0.0022835 | 0.0978639 | 0.3128321 |
| tbats | dy.wk.mo | 2018-04-13 | 1440 | 0.0015214 | 0.0015196 | 0.0421369 | 0.2052728 |
| tbats | dy.wk.mo | 2018-04-14 | 1 | 0.0003214 | 0.0003213 | 0.0011897 | 0.0344924 |
| tbats | dy.wk.mo | 2018-04-16 | 1439 | 0.0012850 | 0.0012857 | 0.0236954 | 0.1539331 |
| tbats | dy.wk.mo | 2018-04-17 | 1440 | 0.0006960 | 0.0006963 | 0.0083356 | 0.0912998 |
| tbats | dy.wk.mo | 2018-04-18 | 1440 | 0.0020360 | 0.0020336 | 0.0561993 | 0.2370638 |
| tbats | dy.wk.mo | 2018-04-19 | 1440 | 0.0012646 | 0.0012637 | 0.0219771 | 0.1482466 |
| tbats | dy.wk.mo | 2018-04-20 | 1440 | 0.0020513 | 0.0020488 | 0.0578264 | 0.2404713 |
| tbats | dy.wk.mo | 2018-04-21 | 1 | 0.0025569 | 0.0025537 | 0.0753680 | 0.2745324 |
| tbats | dy.wk.mo | 2018-04-23 | 1439 | 0.0045574 | 0.0045417 | 0.3641014 | 0.6034082 |
| tbats | dy.wk.mo | 2018-04-24 | 1440 | 0.0011936 | 0.0011923 | 0.0310049 | 0.1760822 |
| tbats | dy.wk.mo | 2018-04-25 | 1440 | 0.0027036 | 0.0026985 | 0.1198454 | 0.3461869 |
| tbats | dy.wk.mo | 2018-04-26 | 1440 | 0.0010284 | 0.0010292 | 0.0189175 | 0.1375410 |
| tbats | dy.wk.mo | 2018-04-27 | 1440 | 0.0008731 | 0.0008737 | 0.0162998 | 0.1276708 |
| tbats | dy.wk.mo | 2018-04-28 | 1 | 0.0022293 | 0.0022318 | 0.0593742 | 0.2436682 |
| tbats | dy.wk.mo | 2018-04-30 | 1439 | 0.0014981 | 0.0014966 | 0.0373015 | 0.1931360 |
| tbats | dy.wk.mo | 2018-05-01 | 1440 | 0.0019013 | 0.0018985 | 0.0693480 | 0.2633402 |
| tbats | dy.wk.mo | 2018-05-02 | 1440 | 0.0006549 | 0.0006552 | 0.0081634 | 0.0903516 |
| tbats | dy.wk.mo | 2018-05-03 | 1440 | 0.0032216 | 0.0032295 | 0.1897824 | 0.4356402 |
| tbats | dy.wk.mo | 2018-05-04 | 1440 | 0.0010331 | 0.0010340 | 0.0206103 | 0.1435629 |
| tbats | dy.wk.mo | 2018-05-05 | 1 | 0.0010655 | 0.0010661 | 0.0135366 | 0.1163469 |
| tbats | dy.wk.mo | 2018-05-07 | 1439 | 0.0010947 | 0.0010942 | 0.0214076 | 0.1463134 |
| tbats | dy.wk.mo | 2018-05-08 | 1440 | 0.0008231 | 0.0008230 | 0.0123015 | 0.1109120 |
| tbats | dy.wk.mo | 2018-05-09 | 1440 | 0.0041063 | 0.0040964 | 0.2378793 | 0.4877287 |
| tbats | dy.wk.mo | 2018-05-10 | 1440 | 0.0013571 | 0.0013583 | 0.0376889 | 0.1941362 |
| tbats | dy.wk.mo | 2018-05-11 | 1440 | 0.0007071 | 0.0007073 | 0.0085426 | 0.0924261 |
| tbats | dy.wk.mo | 2018-05-12 | 1 | 0.0001084 | 0.0001084 | 0.0001407 | 0.0118627 |
| tbats | dy.wk.mo | 2018-05-14 | 1439 | 0.0011015 | 0.0011009 | 0.0199802 | 0.1413512 |
| tbats | dy.wk.mo | 2018-05-15 | 1440 | 0.0030324 | 0.0030251 | 0.1739168 | 0.4170333 |
| tbats | dy.wk.mo | 2018-05-16 | 1440 | 0.0010804 | 0.0010812 | 0.0199944 | 0.1414014 |
| tbats | dy.wk.mo | 2018-05-17 | 1440 | 0.0020307 | 0.0020285 | 0.0654388 | 0.2558101 |
| tbats | dy.wk.mo | 2018-05-18 | 1440 | 0.0011077 | 0.0011070 | 0.0198553 | 0.1409090 |
| tbats | dy.wk.mo | 2018-05-19 | 1 | 0.0001121 | 0.0001121 | 0.0001542 | 0.0124188 |
| tbats | dy.wk.mo | 2018-05-21 | 1439 | 0.0034640 | 0.0034570 | 0.1707487 | 0.4132175 |
| tbats | dy.wk.mo | 2018-05-22 | 1440 | 0.0008634 | 0.0008638 | 0.0115268 | 0.1073628 |
| tbats | dy.wk.mo | 2018-05-23 | 1440 | 0.0057152 | 0.0057369 | 0.5334848 | 0.7304004 |
| tbats | dy.wk.mo | 2018-05-24 | 1440 | 0.0049613 | 0.0049761 | 0.3572843 | 0.5977326 |
| tbats | dy.wk.mo | 2018-05-25 | 1440 | 0.0016297 | 0.0016280 | 0.0431029 | 0.2076123 |
| tbats | dy.wk.mo | 2018-05-26 | 1 | 0.0012197 | 0.0012189 | 0.0177573 | 0.1332567 |
| tbats | dy.wk.mo | 2018-05-28 | 1439 | 0.0008197 | 0.0008190 | 0.0181354 | 0.1346679 |
| tbats | dy.wk.mo | 2018-05-29 | 1440 | 0.0046713 | 0.0046855 | 0.3399934 | 0.5830895 |
| tbats | dy.wk.mo | 2018-05-30 | 1440 | 0.0013350 | 0.0013353 | 0.0273422 | 0.1653547 |
| tbats | dy.wk.mo | 2018-05-31 | 1440 | 0.0015382 | 0.0015399 | 0.0399556 | 0.1998889 |
| tbats | dy.wk.mo | 2018-06-01 | 1440 | 0.0039014 | 0.0038911 | 0.2445897 | 0.4945602 |
| tbats | dy.wk.mo | 2018-06-02 | 1 | 0.0064171 | 0.0063966 | 0.4876375 | 0.6983105 |
| tbats | dy.wk.mo | 2018-06-04 | 1439 | 0.0009632 | 0.0009625 | 0.0173568 | 0.1317451 |
| tbats | dy.wk.mo | 2018-06-05 | 1440 | 0.0006842 | 0.0006843 | 0.0091050 | 0.0954199 |
| tbats | dy.wk.mo | 2018-06-06 | 1440 | 0.0020099 | 0.0020072 | 0.0659765 | 0.2568589 |
| tbats | dy.wk.mo | 2018-06-07 | 1440 | 0.0020891 | 0.0020921 | 0.0743108 | 0.2726002 |
| tbats | dy.wk.mo | 2018-06-08 | 1440 | 0.0016476 | 0.0016495 | 0.0491911 | 0.2217906 |
| tbats | dy.wk.mo | 2018-06-09 | 1 | 0.0015407 | 0.0015419 | 0.0285672 | 0.1690183 |
| tbats | dy.wk.mo | 2018-06-11 | 1439 | 0.0031091 | 0.0031034 | 0.1430100 | 0.3781666 |
| tbats | dy.wk.mo | 2018-06-12 | 1440 | 0.0022452 | 0.0022423 | 0.0699336 | 0.2644497 |
| tbats | dy.wk.mo | 2018-06-13 | 1440 | 0.0013507 | 0.0013493 | 0.0326392 | 0.1806632 |
| tbats | dy.wk.mo | 2018-06-14 | 1440 | 0.0017034 | 0.0017045 | 0.0503907 | 0.2244787 |
| tbats | dy.wk.mo | 2018-06-15 | 1440 | 0.0007262 | 0.0007262 | 0.0098580 | 0.0992877 |
| tbats | dy.wk.mo | 2018-06-16 | 1 | 0.0002990 | 0.0002990 | 0.0010945 | 0.0330835 |
| tbats | dy.wk.mo | 2018-06-18 | 1439 | 0.0014148 | 0.0014160 | 0.0291882 | 0.1708456 |
| tbats | dy.wk.mo | 2018-06-19 | 1440 | 0.0052965 | 0.0053130 | 0.4012069 | 0.6334090 |
| tbats | dy.wk.mo | 2018-06-20 | 1440 | 0.0009220 | 0.0009213 | 0.0190946 | 0.1381832 |
| tbats | dy.wk.mo | 2018-06-21 | 1440 | 0.0019756 | 0.0019765 | 0.0688416 | 0.2623768 |
| tbats | dy.wk.mo | 2018-06-22 | 1440 | 0.0006668 | 0.0006666 | 0.0087552 | 0.0935694 |
| tbats | dy.wk.mo | 2018-06-23 | 1 | 0.0000094 | 0.0000094 | 0.0000011 | 0.0010375 |
| tbats | dy.wk.mo | 2018-06-25 | 1439 | 0.0035453 | 0.0035526 | 0.1749720 | 0.4182966 |
| tbats | dy.wk.mo | 2018-06-26 | 1440 | 0.0016594 | 0.0016593 | 0.0462447 | 0.2150457 |
| tbats | dy.wk.mo | 2018-06-27 | 1440 | 0.0016473 | 0.0016467 | 0.0434331 | 0.2084062 |
| tbats | dy.wk.mo | 2018-06-28 | 1440 | 0.0008683 | 0.0008680 | 0.0167759 | 0.1295220 |
| tbats | dy.wk.mo | 2018-06-29 | 1440 | 0.0015291 | 0.0015275 | 0.0395008 | 0.1987482 |
| tbats | dy.wk.mo | 2018-06-30 | 1 | 0.0017289 | 0.0017274 | 0.0364968 | 0.1910414 |
| tbats | dy.wk.mo | 2018-07-02 | 1439 | 0.0010502 | 0.0010493 | 0.0212129 | 0.1456465 |
| tbats | dy.wk.mo | 2018-07-03 | 1440 | 0.0012721 | 0.0012733 | 0.0349143 | 0.1868537 |
| tbats | dy.wk.mo | 2018-07-04 | 1440 | 0.0010274 | 0.0010281 | 0.0163645 | 0.1279240 |
| tbats | dy.wk.mo | 2018-07-05 | 1440 | 0.0009804 | 0.0009800 | 0.0141517 | 0.1189611 |
| tbats | dy.wk.mo | 2018-07-06 | 1440 | 0.0007993 | 0.0007997 | 0.0130552 | 0.1142594 |
| tbats | dy.wk.mo | 2018-07-07 | 1 | 0.0016373 | 0.0016386 | 0.0328181 | 0.1811577 |
| tbats | dy.yr | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.yr | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.yr | 2018-01-05 | 1440 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| tbats | dy.yr | 2018-01-06 | 1 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| tbats | dy.yr | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050746 | 0.4528517 |
| tbats | dy.yr | 2018-01-09 | 1440 | 0.0012943 | 0.0012931 | 0.0419181 | 0.2047390 |
| tbats | dy.yr | 2018-01-10 | 1440 | 0.0073048 | 0.0073400 | 0.8879488 | 0.9423103 |
| tbats | dy.yr | 2018-01-11 | 1440 | 0.0103775 | 0.0104334 | 1.4110712 | 1.1878852 |
| tbats | dy.yr | 2018-01-12 | 1440 | 0.0130046 | 0.0130904 | 2.1649021 | 1.4713606 |
| tbats | dy.yr | 2018-01-13 | 1 | 0.0147054 | 0.0148143 | 2.7456490 | 1.6570000 |
| tbats | dy.yr | 2018-01-15 | 1439 | 0.0177735 | 0.0179342 | 4.0444477 | 2.0110812 |
| tbats | dy.yr | 2018-01-16 | 1440 | 0.0175204 | 0.0176763 | 3.9235329 | 1.9807910 |
| tbats | dy.yr | 2018-01-17 | 1440 | 0.0173391 | 0.0174925 | 3.8604893 | 1.9648128 |
| tbats | dy.yr | 2018-01-18 | 1440 | 0.0132828 | 0.0133725 | 2.2636575 | 1.5045456 |
| tbats | dy.yr | 2018-01-19 | 1440 | 0.0169647 | 0.0171110 | 3.6821392 | 1.9188901 |
| tbats | dy.yr | 2018-01-20 | 1 | 0.0163738 | 0.0165090 | 3.4040250 | 1.8450000 |
| tbats | dy.yr | 2018-01-22 | 1439 | 0.0164475 | 0.0165846 | 3.4523110 | 1.8580396 |
| tbats | dy.yr | 2018-01-23 | 1440 | 0.0180156 | 0.0181820 | 4.1856644 | 2.0458896 |
| tbats | dy.yr | 2018-01-24 | 1440 | 0.0268881 | 0.0272614 | 9.3470597 | 3.0572961 |
| tbats | dy.yr | 2018-01-25 | 1440 | 0.0322722 | 0.0328036 | 13.2754674 | 3.6435515 |
| tbats | dy.yr | 2018-01-26 | 1440 | 0.0318377 | 0.0323591 | 13.0263583 | 3.6092047 |
| tbats | dy.yr | 2018-01-27 | 1 | 0.0359514 | 0.0366094 | 16.4106010 | 4.0510000 |
| tbats | dy.yr | 2018-01-29 | 1439 | 0.0339983 | 0.0345871 | 14.6966838 | 3.8336254 |
| tbats | dy.yr | 2018-01-30 | 1440 | 0.0346458 | 0.0352574 | 15.2604667 | 3.9064647 |
| tbats | dy.yr | 2018-01-31 | 1440 | 0.0333584 | 0.0339260 | 14.1707246 | 3.7644023 |
| tbats | dy.yr | 2018-02-01 | 1440 | 0.0288410 | 0.0292640 | 10.5843271 | 3.2533563 |
| tbats | dy.yr | 2018-02-02 | 1440 | 0.0249175 | 0.0252362 | 7.9895620 | 2.8265813 |
| tbats | dy.yr | 2018-02-03 | 1 | 0.0222400 | 0.0224901 | 6.2800360 | 2.5060000 |
| tbats | dy.yr | 2018-02-05 | 1439 | 0.0247250 | 0.0250364 | 7.8101566 | 2.7946657 |
| tbats | dy.yr | 2018-02-06 | 1440 | 0.0316136 | 0.0321241 | 12.7564999 | 3.5716243 |
| tbats | dy.yr | 2018-02-07 | 1440 | 0.0298147 | 0.0302673 | 11.3204578 | 3.3645888 |
| tbats | dy.yr | 2018-02-08 | 1440 | 0.0295570 | 0.0300045 | 11.1915858 | 3.3453828 |
| tbats | dy.yr | 2018-02-09 | 1440 | 0.0340752 | 0.0346683 | 14.8008132 | 3.8471825 |
| tbats | dy.yr | 2018-02-10 | 1 | 0.0344693 | 0.0350738 | 15.0854560 | 3.8840000 |
| tbats | dy.yr | 2018-02-12 | 1439 | 0.0355512 | 0.0361948 | 16.0525253 | 4.0065603 |
| tbats | dy.yr | 2018-02-13 | 1440 | 0.0415012 | 0.0423895 | 22.0797777 | 4.6989124 |
| tbats | dy.yr | 2018-02-14 | 1440 | 0.0478455 | 0.0490216 | 29.1477209 | 5.3988629 |
| tbats | dy.yr | 2018-02-15 | 1440 | 0.0548283 | 0.0563755 | 38.2107906 | 6.1814877 |
| tbats | dy.yr | 2018-02-16 | 1440 | 0.0585071 | 0.0602717 | 43.4960112 | 6.5951506 |
| tbats | dy.yr | 2018-02-17 | 1 | 0.0565673 | 0.0582138 | 40.6278760 | 6.3740000 |
| tbats | dy.yr | 2018-02-19 | 1439 | 0.0550766 | 0.0566373 | 38.5369395 | 6.2078128 |
| tbats | dy.yr | 2018-02-20 | 1440 | 0.0503269 | 0.0516282 | 32.2105882 | 5.6754373 |
| tbats | dy.yr | 2018-02-21 | 1440 | 0.0451023 | 0.0461438 | 25.8503062 | 5.0843196 |
| tbats | dy.yr | 2018-02-22 | 1440 | 0.0486687 | 0.0498868 | 30.1747998 | 5.4931594 |
| tbats | dy.yr | 2018-02-23 | 1440 | 0.0520678 | 0.0534602 | 34.4368323 | 5.8682904 |
| tbats | dy.yr | 2018-02-24 | 1 | 0.0513756 | 0.0527301 | 33.5125210 | 5.7890000 |
| tbats | dy.yr | 2018-02-26 | 1439 | 0.0523297 | 0.0537373 | 34.8061849 | 5.8996767 |
| tbats | dy.yr | 2018-02-27 | 1440 | 0.0495722 | 0.0508339 | 31.2421536 | 5.5894681 |
| tbats | dy.yr | 2018-02-28 | 1440 | 0.0500147 | 0.0512998 | 31.8154528 | 5.6405188 |
| tbats | dy.yr | 2018-03-01 | 1440 | 0.0528801 | 0.0543178 | 35.5425360 | 5.9617561 |
| tbats | dy.yr | 2018-03-02 | 1440 | 0.0614139 | 0.0633632 | 47.9736591 | 6.9263020 |
| tbats | dy.yr | 2018-03-03 | 1 | 0.0617146 | 0.0636796 | 48.3581160 | 6.9540000 |
| tbats | dy.yr | 2018-03-05 | 1439 | 0.0618393 | 0.0638152 | 48.6191767 | 6.9727453 |
| tbats | dy.yr | 2018-03-06 | 1440 | 0.0576352 | 0.0593462 | 42.1946350 | 6.4957398 |
| tbats | dy.yr | 2018-03-07 | 1440 | 0.0611436 | 0.0630732 | 47.4988149 | 6.8919384 |
| tbats | dy.yr | 2018-03-08 | 1440 | 0.0583970 | 0.0601537 | 43.3046139 | 6.5806241 |
| tbats | dy.yr | 2018-03-09 | 1440 | 0.0528147 | 0.0542485 | 35.4452447 | 5.9535909 |
| tbats | dy.yr | 2018-03-10 | 1 | 0.0519302 | 0.0533146 | 34.2400523 | 5.8515000 |
| tbats | dy.yr | 2018-03-12 | 1439 | 0.0539580 | 0.0554551 | 36.9899617 | 6.0819373 |
| tbats | dy.yr | 2018-03-13 | 1440 | 0.0530344 | 0.0544823 | 35.7881548 | 5.9823202 |
| tbats | dy.yr | 2018-03-14 | 1440 | 0.0552759 | 0.0568478 | 38.8117093 | 6.2299044 |
| tbats | dy.yr | 2018-03-15 | 1440 | 0.0586386 | 0.0604106 | 43.6777665 | 6.6089157 |
| tbats | dy.yr | 2018-03-16 | 1440 | 0.0593666 | 0.0611845 | 44.7900387 | 6.6925360 |
| tbats | dy.yr | 2018-03-17 | 1 | 0.0594382 | 0.0612588 | 44.8565063 | 6.6975000 |
| tbats | dy.yr | 2018-03-19 | 1439 | 0.0596944 | 0.0615318 | 45.2649130 | 6.7279204 |
| tbats | dy.yr | 2018-03-20 | 1440 | 0.0564654 | 0.0581070 | 40.5082290 | 6.3646075 |
| tbats | dy.yr | 2018-03-21 | 1440 | 0.0561626 | 0.0577863 | 40.0706968 | 6.3301419 |
| tbats | dy.yr | 2018-03-22 | 1440 | 0.0620814 | 0.0640717 | 48.9713686 | 6.9979546 |
| tbats | dy.yr | 2018-03-23 | 1440 | 0.0686503 | 0.0710915 | 59.8598804 | 7.7369167 |
| tbats | dy.yr | 2018-03-24 | 1 | 0.0705005 | 0.0730765 | 63.1071360 | 7.9440000 |
| tbats | dy.yr | 2018-03-26 | 1439 | 0.0678501 | 0.0702341 | 58.4820533 | 7.6473560 |
| tbats | dy.yr | 2018-03-27 | 1440 | 0.0627230 | 0.0647543 | 49.9636189 | 7.0684948 |
| tbats | dy.yr | 2018-03-28 | 1440 | 0.0600072 | 0.0618740 | 45.9681799 | 6.7799838 |
| tbats | dy.yr | 2018-03-29 | 1440 | 0.0542516 | 0.0557653 | 37.3936332 | 6.1150334 |
| tbats | dy.yr | 2018-03-30 | 1440 | 0.0569742 | 0.0586453 | 41.2251844 | 6.4206841 |
| tbats | dy.yr | 2018-03-31 | 1 | 0.0567403 | 0.0583971 | 40.8768423 | 6.3935000 |
| tbats | dy.yr | 2018-04-02 | 1439 | 0.0573346 | 0.0590282 | 41.7708572 | 6.4630378 |
| tbats | dy.yr | 2018-04-03 | 1440 | 0.0578294 | 0.0595547 | 42.5392525 | 6.5222122 |
| tbats | dy.yr | 2018-04-04 | 1440 | 0.0551418 | 0.0567069 | 38.6452777 | 6.2165326 |
| tbats | dy.yr | 2018-04-05 | 1440 | 0.0496996 | 0.0509684 | 31.4156586 | 5.6049673 |
| tbats | dy.yr | 2018-04-06 | 1440 | 0.0486093 | 0.0498215 | 30.0316667 | 5.4801156 |
| tbats | dy.yr | 2018-04-07 | 1 | 0.0509585 | 0.0522908 | 32.9705640 | 5.7420000 |
| tbats | dy.yr | 2018-04-09 | 1439 | 0.0505655 | 0.0518776 | 32.4760320 | 5.6987746 |
| tbats | dy.yr | 2018-04-10 | 1440 | 0.0500467 | 0.0513325 | 31.8318784 | 5.6419747 |
| tbats | dy.yr | 2018-04-11 | 1440 | 0.0505795 | 0.0518926 | 32.5015772 | 5.7010155 |
| tbats | dy.yr | 2018-04-12 | 1440 | 0.0500981 | 0.0513869 | 31.9055113 | 5.6484964 |
| tbats | dy.yr | 2018-04-13 | 1440 | 0.0462221 | 0.0473164 | 27.1456958 | 5.2101531 |
| tbats | dy.yr | 2018-04-14 | 1 | 0.0472533 | 0.0483967 | 28.3503003 | 5.3245000 |
| tbats | dy.yr | 2018-04-16 | 1439 | 0.0480113 | 0.0491929 | 29.2834761 | 5.4114209 |
| tbats | dy.yr | 2018-04-17 | 1440 | 0.0499536 | 0.0512334 | 31.6868643 | 5.6291087 |
| tbats | dy.yr | 2018-04-18 | 1440 | 0.0484214 | 0.0496232 | 29.7780866 | 5.4569301 |
| tbats | dy.yr | 2018-04-19 | 1440 | 0.0471391 | 0.0482772 | 28.2180613 | 5.3120675 |
| tbats | dy.yr | 2018-04-20 | 1440 | 0.0451939 | 0.0462391 | 25.9423588 | 5.0933642 |
| tbats | dy.yr | 2018-04-21 | 1 | 0.0447107 | 0.0457331 | 25.3814440 | 5.0380000 |
| tbats | dy.yr | 2018-04-23 | 1439 | 0.0403732 | 0.0412102 | 20.8190835 | 4.5627934 |
| tbats | dy.yr | 2018-04-24 | 1440 | 0.0342189 | 0.0348152 | 14.8829677 | 3.8578450 |
| tbats | dy.yr | 2018-04-25 | 1440 | 0.0316863 | 0.0321978 | 12.7813704 | 3.5751042 |
| tbats | dy.yr | 2018-04-26 | 1440 | 0.0298544 | 0.0303070 | 11.3227741 | 3.3649330 |
| tbats | dy.yr | 2018-04-27 | 1440 | 0.0305881 | 0.0310636 | 11.8910975 | 3.4483471 |
| tbats | dy.yr | 2018-04-28 | 1 | 0.0321441 | 0.0326692 | 13.1188840 | 3.6220000 |
| tbats | dy.yr | 2018-04-30 | 1439 | 0.0306979 | 0.0311769 | 11.9756958 | 3.4605918 |
| tbats | dy.yr | 2018-05-01 | 1440 | 0.0279642 | 0.0283622 | 9.9632937 | 3.1564685 |
| tbats | dy.yr | 2018-05-02 | 1440 | 0.0253920 | 0.0257187 | 8.1921161 | 2.8621873 |
| tbats | dy.yr | 2018-05-03 | 1440 | 0.0283529 | 0.0287634 | 10.2724713 | 3.2050696 |
| tbats | dy.yr | 2018-05-04 | 1440 | 0.0319213 | 0.0324394 | 12.9459186 | 3.5980437 |
| tbats | dy.yr | 2018-05-05 | 1 | 0.0319799 | 0.0324996 | 12.9852123 | 3.6035000 |
| tbats | dy.yr | 2018-05-07 | 1439 | 0.0314228 | 0.0319251 | 12.5540949 | 3.5431758 |
| tbats | dy.yr | 2018-05-08 | 1440 | 0.0322355 | 0.0327640 | 13.2033796 | 3.6336455 |
| tbats | dy.yr | 2018-05-09 | 1440 | 0.0276971 | 0.0280882 | 9.7920757 | 3.1292292 |
| tbats | dy.yr | 2018-05-10 | 1440 | 0.0268879 | 0.0272554 | 9.2076423 | 3.0344097 |
| tbats | dy.yr | 2018-05-11 | 1440 | 0.0295278 | 0.0299706 | 11.0766470 | 3.3281597 |
| tbats | dy.yr | 2018-05-12 | 1 | 0.0292332 | 0.0296669 | 10.8504360 | 3.2940000 |
| tbats | dy.yr | 2018-05-14 | 1439 | 0.0285502 | 0.0289643 | 10.3633711 | 3.2192190 |
| tbats | dy.yr | 2018-05-15 | 1440 | 0.0238221 | 0.0241119 | 7.2687680 | 2.6960653 |
| tbats | dy.yr | 2018-05-16 | 1440 | 0.0217231 | 0.0219618 | 5.9972995 | 2.4489384 |
| tbats | dy.yr | 2018-05-17 | 1440 | 0.0190188 | 0.0192032 | 4.6376754 | 2.1535263 |
| tbats | dy.yr | 2018-05-18 | 1440 | 0.0162332 | 0.0163665 | 3.3582588 | 1.8325553 |
| tbats | dy.yr | 2018-05-19 | 1 | 0.0171015 | 0.0172490 | 3.7133290 | 1.9270000 |
| tbats | dy.yr | 2018-05-21 | 1439 | 0.0136949 | 0.0137903 | 2.4048528 | 1.5507588 |
| tbats | dy.yr | 2018-05-22 | 1440 | 0.0152313 | 0.0153483 | 2.9492781 | 1.7173462 |
| tbats | dy.yr | 2018-05-23 | 1440 | 0.0214290 | 0.0216665 | 5.9628655 | 2.4418979 |
| tbats | dy.yr | 2018-05-24 | 1440 | 0.0278934 | 0.0282903 | 9.9377873 | 3.1524256 |
| tbats | dy.yr | 2018-05-25 | 1440 | 0.0289092 | 0.0293338 | 10.6257407 | 3.2597148 |
| tbats | dy.yr | 2018-05-26 | 1 | 0.0292155 | 0.0296486 | 10.8372640 | 3.2920000 |
| tbats | dy.yr | 2018-05-28 | 1439 | 0.0287038 | 0.0291224 | 10.4758182 | 3.2366369 |
| tbats | dy.yr | 2018-05-29 | 1440 | 0.0334591 | 0.0340318 | 14.2958765 | 3.7809888 |
| tbats | dy.yr | 2018-05-30 | 1440 | 0.0348500 | 0.0354691 | 15.4474376 | 3.9303228 |
| tbats | dy.yr | 2018-05-31 | 1440 | 0.0349467 | 0.0355687 | 15.5187281 | 3.9393817 |
| tbats | dy.yr | 2018-06-01 | 1440 | 0.0305646 | 0.0310420 | 11.9334252 | 3.4544790 |
| tbats | dy.yr | 2018-06-02 | 1 | 0.0280529 | 0.0284520 | 9.9919210 | 3.1610000 |
| tbats | dy.yr | 2018-06-04 | 1439 | 0.0272565 | 0.0276335 | 9.4419288 | 3.0727722 |
| tbats | dy.yr | 2018-06-05 | 1440 | 0.0256171 | 0.0259498 | 8.3406851 | 2.8880244 |
| tbats | dy.yr | 2018-06-06 | 1440 | 0.0236709 | 0.0239552 | 7.1314719 | 2.6704816 |
| tbats | dy.yr | 2018-06-07 | 1440 | 0.0241939 | 0.0244910 | 7.4534678 | 2.7301040 |
| tbats | dy.yr | 2018-06-08 | 1440 | 0.0278386 | 0.0282325 | 9.8637981 | 3.1406684 |
| tbats | dy.yr | 2018-06-09 | 1 | 0.0279331 | 0.0283287 | 9.9067563 | 3.1475000 |
| tbats | dy.yr | 2018-06-11 | 1439 | 0.0253705 | 0.0256989 | 8.2308141 | 2.8689395 |
| tbats | dy.yr | 2018-06-12 | 1440 | 0.0213017 | 0.0215314 | 5.7706147 | 2.4022104 |
| tbats | dy.yr | 2018-06-13 | 1440 | 0.0191762 | 0.0193623 | 4.6803909 | 2.1634211 |
| tbats | dy.yr | 2018-06-14 | 1440 | 0.0215490 | 0.0217855 | 5.9378640 | 2.4367733 |
| tbats | dy.yr | 2018-06-15 | 1440 | 0.0182994 | 0.0184688 | 4.2613323 | 2.0642995 |
| tbats | dy.yr | 2018-06-16 | 1 | 0.0178781 | 0.0180393 | 4.0582102 | 2.0145000 |
| tbats | dy.yr | 2018-06-18 | 1439 | 0.0192425 | 0.0194297 | 4.7069267 | 2.1695453 |
| tbats | dy.yr | 2018-06-19 | 1440 | 0.0241006 | 0.0243970 | 7.4340138 | 2.7265388 |
| tbats | dy.yr | 2018-06-20 | 1440 | 0.0224995 | 0.0227559 | 6.4389355 | 2.5375058 |
| tbats | dy.yr | 2018-06-21 | 1440 | 0.0208018 | 0.0210232 | 5.5623215 | 2.3584574 |
| tbats | dy.yr | 2018-06-22 | 1440 | 0.0236769 | 0.0239609 | 7.1257653 | 2.6694129 |
| tbats | dy.yr | 2018-06-23 | 1 | 0.0238995 | 0.0241886 | 7.2522490 | 2.6930000 |
| tbats | dy.yr | 2018-06-25 | 1439 | 0.0273632 | 0.0277437 | 9.5296900 | 3.0870196 |
| tbats | dy.yr | 2018-06-26 | 1440 | 0.0261115 | 0.0264588 | 8.7023493 | 2.9499745 |
| tbats | dy.yr | 2018-06-27 | 1440 | 0.0231693 | 0.0234426 | 6.8580605 | 2.6187899 |
| tbats | dy.yr | 2018-06-28 | 1440 | 0.0212360 | 0.0214646 | 5.7420078 | 2.3962487 |
| tbats | dy.yr | 2018-06-29 | 1440 | 0.0179686 | 0.0181321 | 4.1138114 | 2.0282533 |
| tbats | dy.yr | 2018-06-30 | 1 | 0.0176784 | 0.0178360 | 3.9680640 | 1.9920000 |
| tbats | dy.yr | 2018-07-02 | 1439 | 0.0166676 | 0.0168080 | 3.5355166 | 1.8802969 |
| tbats | dy.yr | 2018-07-03 | 1440 | 0.0167358 | 0.0168780 | 3.5806198 | 1.8922526 |
| tbats | dy.yr | 2018-07-04 | 1440 | 0.0196316 | 0.0198264 | 4.8968547 | 2.2128838 |
| tbats | dy.yr | 2018-07-05 | 1440 | 0.0009931 | 0.0009929 | 0.0174183 | 0.1319785 |
| tbats | dy.yr | 2018-07-06 | 1440 | 0.0007986 | 0.0007990 | 0.0130234 | 0.1141202 |
| tbats | dy.yr | 2018-07-07 | 1 | 0.0016348 | 0.0016361 | 0.0327167 | 0.1808775 |
| ts | mo.1440 | 2018-01-03 | 1439 | 0.0006195 | 0.0006192 | 0.0089053 | 0.0943678 |
| ts | mo.1440 | 2018-01-04 | 1440 | 0.0018933 | 0.0018912 | 0.0524653 | 0.2290530 |
| ts | mo.1440 | 2018-01-05 | 1440 | 0.0026655 | 0.0026607 | 0.1209434 | 0.3477691 |
| ts | mo.1440 | 2018-01-06 | 1 | 0.0028170 | 0.0028130 | 0.1008702 | 0.3176007 |
| ts | mo.1440 | 2018-01-08 | 1439 | 0.0006855 | 0.0006853 | 0.0096424 | 0.0981956 |
| ts | mo.1440 | 2018-01-09 | 1440 | 0.0033514 | 0.0033582 | 0.1742534 | 0.4174367 |
| ts | mo.1440 | 2018-01-10 | 1440 | 0.0068046 | 0.0068360 | 0.7940909 | 0.8911178 |
| ts | mo.1440 | 2018-01-11 | 1440 | 0.0021101 | 0.0021080 | 0.0753938 | 0.2745793 |
| ts | mo.1440 | 2018-01-12 | 1440 | 0.0009539 | 0.0009540 | 0.0195391 | 0.1397822 |
| ts | mo.1440 | 2018-01-13 | 1 | 0.0020477 | 0.0020498 | 0.0518981 | 0.2278115 |
| ts | mo.1440 | 2018-01-15 | 1439 | 0.0031322 | 0.0031379 | 0.1405843 | 0.3749457 |
| ts | mo.1440 | 2018-01-16 | 1440 | 0.0019964 | 0.0019941 | 0.0615712 | 0.2481354 |
| ts | mo.1440 | 2018-01-17 | 1440 | 0.0025769 | 0.0025725 | 0.1147781 | 0.3387891 |
| ts | mo.1440 | 2018-01-18 | 1440 | 0.0011133 | 0.0011144 | 0.0300424 | 0.1733274 |
| ts | mo.1440 | 2018-01-19 | 1440 | 0.0032498 | 0.0032559 | 0.1518261 | 0.3896487 |
| ts | mo.1440 | 2018-01-20 | 1 | 0.0025869 | 0.0025903 | 0.0826358 | 0.2874644 |
| ts | mo.1440 | 2018-01-22 | 1439 | 0.0011021 | 0.0011013 | 0.0292844 | 0.1711268 |
| ts | mo.1440 | 2018-01-23 | 1440 | 0.0024768 | 0.0024813 | 0.1120652 | 0.3347614 |
| ts | mo.1440 | 2018-01-24 | 1440 | 0.0056818 | 0.0057036 | 0.5273406 | 0.7261822 |
| ts | mo.1440 | 2018-01-25 | 1440 | 0.0017824 | 0.0017840 | 0.0590921 | 0.2430887 |
| ts | mo.1440 | 2018-01-26 | 1440 | 0.0029631 | 0.0029692 | 0.1731140 | 0.4160698 |
| ts | mo.1440 | 2018-01-27 | 1 | 0.0071288 | 0.0071543 | 0.6083229 | 0.7799506 |
| ts | mo.1440 | 2018-01-29 | 1439 | 0.0026183 | 0.0026131 | 0.1226401 | 0.3502001 |
| ts | mo.1440 | 2018-01-30 | 1440 | 0.0014954 | 0.0014969 | 0.0368227 | 0.1918925 |
| ts | mo.1440 | 2018-01-31 | 1440 | 0.0020807 | 0.0020765 | 0.1022261 | 0.3197282 |
| ts | mo.1440 | 2018-02-01 | 1440 | 0.0027513 | 0.0027460 | 0.1272960 | 0.3567856 |
| ts | mo.1440 | 2018-02-02 | 1440 | 0.0045591 | 0.0045437 | 0.3712070 | 0.6092676 |
| ts | mo.1440 | 2018-02-03 | 1 | 0.0070416 | 0.0070169 | 0.5934794 | 0.7703762 |
| ts | mo.1440 | 2018-02-05 | 1439 | 0.0027148 | 0.0027202 | 0.1318728 | 0.3631429 |
| ts | mo.1440 | 2018-02-06 | 1440 | 0.0019095 | 0.0019104 | 0.0742091 | 0.2724135 |
| ts | mo.1440 | 2018-02-07 | 1440 | 0.0022077 | 0.0022110 | 0.0816195 | 0.2856913 |
| ts | mo.1440 | 2018-02-08 | 1440 | 0.0027822 | 0.0027830 | 0.1338333 | 0.3658324 |
| ts | mo.1440 | 2018-02-09 | 1440 | 0.0020346 | 0.0020348 | 0.0735302 | 0.2711646 |
| ts | mo.1440 | 2018-02-10 | 1 | 0.0004782 | 0.0004781 | 0.0027043 | 0.0520031 |
| ts | mo.1440 | 2018-02-12 | 1439 | 0.0015525 | 0.0015542 | 0.0399390 | 0.1998473 |
| ts | mo.1440 | 2018-02-13 | 1440 | 0.0066730 | 0.0067043 | 0.7404211 | 0.8604773 |
| ts | mo.1440 | 2018-02-14 | 1440 | 0.0047852 | 0.0048002 | 0.3478155 | 0.5897589 |
| ts | mo.1440 | 2018-02-15 | 1440 | 0.0045488 | 0.0045610 | 0.2795891 | 0.5287619 |
| ts | mo.1440 | 2018-02-16 | 1440 | 0.0011755 | 0.0011760 | 0.0261509 | 0.1617124 |
| ts | mo.1440 | 2018-02-17 | 1 | 0.0016106 | 0.0016093 | 0.0292211 | 0.1709417 |
| ts | mo.1440 | 2018-02-19 | 1439 | 0.0023436 | 0.0023402 | 0.0782012 | 0.2796448 |
| ts | mo.1440 | 2018-02-20 | 1440 | 0.0043016 | 0.0042902 | 0.2594391 | 0.5093516 |
| ts | mo.1440 | 2018-02-21 | 1440 | 0.0028693 | 0.0028638 | 0.1267526 | 0.3560234 |
| ts | mo.1440 | 2018-02-22 | 1440 | 0.0050996 | 0.0051170 | 0.4014508 | 0.6336014 |
| ts | mo.1440 | 2018-02-23 | 1440 | 0.0012161 | 0.0012151 | 0.0268283 | 0.1637934 |
| ts | mo.1440 | 2018-02-24 | 1 | 0.0012834 | 0.0012826 | 0.0187718 | 0.1370103 |
| ts | mo.1440 | 2018-02-26 | 1439 | 0.0017900 | 0.0017912 | 0.0471587 | 0.2171605 |
| ts | mo.1440 | 2018-02-27 | 1440 | 0.0020308 | 0.0020271 | 0.0870698 | 0.2950759 |
| ts | mo.1440 | 2018-02-28 | 1440 | 0.0025601 | 0.0025654 | 0.1226653 | 0.3502360 |
| ts | mo.1440 | 2018-03-01 | 1440 | 0.0016189 | 0.0016184 | 0.0454563 | 0.2132049 |
| ts | mo.1440 | 2018-03-02 | 1440 | 0.0048308 | 0.0048463 | 0.3484952 | 0.5903348 |
| ts | mo.1440 | 2018-03-03 | 1 | 0.0047455 | 0.0047568 | 0.2541284 | 0.5041115 |
| ts | mo.1440 | 2018-03-05 | 1439 | 0.0017973 | 0.0017957 | 0.0613283 | 0.2476455 |
| ts | mo.1440 | 2018-03-06 | 1440 | 0.0011799 | 0.0011796 | 0.0240326 | 0.1550244 |
| ts | mo.1440 | 2018-03-07 | 1440 | 0.0029808 | 0.0029865 | 0.1275201 | 0.3570996 |
| ts | mo.1440 | 2018-03-08 | 1440 | 0.0011034 | 0.0011026 | 0.0179415 | 0.1339457 |
| ts | mo.1440 | 2018-03-09 | 1440 | 0.0055607 | 0.0055439 | 0.3783486 | 0.6151004 |
| ts | mo.1440 | 2018-03-10 | 1 | 0.0057301 | 0.0057137 | 0.3704495 | 0.6086456 |
| ts | mo.1440 | 2018-03-12 | 1439 | 0.0020550 | 0.0020577 | 0.0631336 | 0.2512641 |
| ts | mo.1440 | 2018-03-13 | 1440 | 0.0033638 | 0.0033549 | 0.2066242 | 0.4545593 |
| ts | mo.1440 | 2018-03-14 | 1440 | 0.0013668 | 0.0013683 | 0.0358629 | 0.1893749 |
| ts | mo.1440 | 2018-03-15 | 1440 | 0.0023583 | 0.0023619 | 0.0818605 | 0.2861128 |
| ts | mo.1440 | 2018-03-16 | 1440 | 0.0029534 | 0.0029595 | 0.1367507 | 0.3697982 |
| ts | mo.1440 | 2018-03-17 | 1 | 0.0033997 | 0.0034055 | 0.1307075 | 0.3615350 |
| ts | mo.1440 | 2018-03-19 | 1439 | 0.0009580 | 0.0009578 | 0.0155765 | 0.1248059 |
| ts | mo.1440 | 2018-03-20 | 1440 | 0.0027241 | 0.0027197 | 0.1017598 | 0.3189981 |
| ts | mo.1440 | 2018-03-21 | 1440 | 0.0015818 | 0.0015840 | 0.0511097 | 0.2260745 |
| ts | mo.1440 | 2018-03-22 | 1440 | 0.0031871 | 0.0031939 | 0.1531523 | 0.3913467 |
| ts | mo.1440 | 2018-03-23 | 1440 | 0.0029535 | 0.0029586 | 0.1137222 | 0.3372273 |
| ts | mo.1440 | 2018-03-24 | 1 | 0.0051860 | 0.0051995 | 0.2981093 | 0.5459939 |
| ts | mo.1440 | 2018-03-26 | 1439 | 0.0032447 | 0.0032384 | 0.1373792 | 0.3706470 |
| ts | mo.1440 | 2018-03-27 | 1440 | 0.0024021 | 0.0023986 | 0.0768881 | 0.2772870 |
| ts | mo.1440 | 2018-03-28 | 1440 | 0.0051964 | 0.0051729 | 0.5236254 | 0.7236196 |
| ts | mo.1440 | 2018-03-29 | 1440 | 0.0026082 | 0.0026127 | 0.1093110 | 0.3306221 |
| ts | mo.1440 | 2018-03-30 | 1440 | 0.0016661 | 0.0016677 | 0.0383483 | 0.1958271 |
| ts | mo.1440 | 2018-03-31 | 1 | 0.0013534 | 0.0013543 | 0.0207494 | 0.1440466 |
| ts | mo.1440 | 2018-04-02 | 1439 | 0.0015342 | 0.0015357 | 0.0505865 | 0.2249144 |
| ts | mo.1440 | 2018-04-03 | 1440 | 0.0027881 | 0.0027819 | 0.1417164 | 0.3764524 |
| ts | mo.1440 | 2018-04-04 | 1440 | 0.0015284 | 0.0015305 | 0.0542717 | 0.2329628 |
| ts | mo.1440 | 2018-04-05 | 1440 | 0.0034683 | 0.0034604 | 0.1816545 | 0.4262094 |
| ts | mo.1440 | 2018-04-06 | 1440 | 0.0017739 | 0.0017764 | 0.0625194 | 0.2500388 |
| ts | mo.1440 | 2018-04-07 | 1 | 0.0041446 | 0.0041532 | 0.1980759 | 0.4450571 |
| ts | mo.1440 | 2018-04-09 | 1439 | 0.0012144 | 0.0012137 | 0.0240610 | 0.1551160 |
| ts | mo.1440 | 2018-04-10 | 1440 | 0.0027224 | 0.0027177 | 0.1076017 | 0.3280269 |
| ts | mo.1440 | 2018-04-11 | 1440 | 0.0020798 | 0.0020828 | 0.0707359 | 0.2659621 |
| ts | mo.1440 | 2018-04-12 | 1440 | 0.0023498 | 0.0023454 | 0.0995258 | 0.3154771 |
| ts | mo.1440 | 2018-04-13 | 1440 | 0.0014644 | 0.0014626 | 0.0411205 | 0.2027819 |
| ts | mo.1440 | 2018-04-14 | 1 | 0.0003313 | 0.0003313 | 0.0012645 | 0.0355595 |
| ts | mo.1440 | 2018-04-16 | 1439 | 0.0016840 | 0.0016851 | 0.0369468 | 0.1922154 |
| ts | mo.1440 | 2018-04-17 | 1440 | 0.0008842 | 0.0008848 | 0.0127984 | 0.1131300 |
| ts | mo.1440 | 2018-04-18 | 1440 | 0.0018057 | 0.0018037 | 0.0461242 | 0.2147655 |
| ts | mo.1440 | 2018-04-19 | 1440 | 0.0008831 | 0.0008826 | 0.0120799 | 0.1099087 |
| ts | mo.1440 | 2018-04-20 | 1440 | 0.0015960 | 0.0015944 | 0.0358682 | 0.1893889 |
| ts | mo.1440 | 2018-04-21 | 1 | 0.0025516 | 0.0025484 | 0.0750545 | 0.2739607 |
| ts | mo.1440 | 2018-04-23 | 1439 | 0.0040202 | 0.0040065 | 0.3198618 | 0.5655633 |
| ts | mo.1440 | 2018-04-24 | 1440 | 0.0008583 | 0.0008575 | 0.0187194 | 0.1368189 |
| ts | mo.1440 | 2018-04-25 | 1440 | 0.0023138 | 0.0023097 | 0.0966523 | 0.3108895 |
| ts | mo.1440 | 2018-04-26 | 1440 | 0.0013040 | 0.0013052 | 0.0297695 | 0.1725384 |
| ts | mo.1440 | 2018-04-27 | 1440 | 0.0009764 | 0.0009771 | 0.0201477 | 0.1419426 |
| ts | mo.1440 | 2018-04-28 | 1 | 0.0022244 | 0.0022269 | 0.0591127 | 0.2431310 |
| ts | mo.1440 | 2018-04-30 | 1439 | 0.0013327 | 0.0013315 | 0.0303145 | 0.1741105 |
| ts | mo.1440 | 2018-05-01 | 1440 | 0.0018094 | 0.0018068 | 0.0636654 | 0.2523201 |
| ts | mo.1440 | 2018-05-02 | 1440 | 0.0006189 | 0.0006191 | 0.0066997 | 0.0818516 |
| ts | mo.1440 | 2018-05-03 | 1440 | 0.0031605 | 0.0031684 | 0.1900204 | 0.4359133 |
| ts | mo.1440 | 2018-05-04 | 1440 | 0.0008358 | 0.0008365 | 0.0152062 | 0.1233134 |
| ts | mo.1440 | 2018-05-05 | 1 | 0.0010685 | 0.0010691 | 0.0136127 | 0.1166735 |
| ts | mo.1440 | 2018-05-07 | 1439 | 0.0011199 | 0.0011192 | 0.0223430 | 0.1494757 |
| ts | mo.1440 | 2018-05-08 | 1440 | 0.0007801 | 0.0007804 | 0.0113551 | 0.1065603 |
| ts | mo.1440 | 2018-05-09 | 1440 | 0.0043041 | 0.0042934 | 0.2581366 | 0.5080715 |
| ts | mo.1440 | 2018-05-10 | 1440 | 0.0013982 | 0.0013996 | 0.0390151 | 0.1975224 |
| ts | mo.1440 | 2018-05-11 | 1440 | 0.0008709 | 0.0008713 | 0.0130281 | 0.1141405 |
| ts | mo.1440 | 2018-05-12 | 1 | 0.0001085 | 0.0001085 | 0.0001409 | 0.0118714 |
| ts | mo.1440 | 2018-05-14 | 1439 | 0.0009962 | 0.0009955 | 0.0193733 | 0.1391880 |
| ts | mo.1440 | 2018-05-15 | 1440 | 0.0030133 | 0.0030060 | 0.1755404 | 0.4189754 |
| ts | mo.1440 | 2018-05-16 | 1440 | 0.0011822 | 0.0011831 | 0.0246931 | 0.1571405 |
| ts | mo.1440 | 2018-05-17 | 1440 | 0.0020354 | 0.0020327 | 0.0716848 | 0.2677401 |
| ts | mo.1440 | 2018-05-18 | 1440 | 0.0011898 | 0.0011889 | 0.0243060 | 0.1559038 |
| ts | mo.1440 | 2018-05-19 | 1 | 0.0001146 | 0.0001146 | 0.0001611 | 0.0126927 |
| ts | mo.1440 | 2018-05-21 | 1439 | 0.0035841 | 0.0035769 | 0.1765591 | 0.4201893 |
| ts | mo.1440 | 2018-05-22 | 1440 | 0.0010873 | 0.0010880 | 0.0188758 | 0.1373891 |
| ts | mo.1440 | 2018-05-23 | 1440 | 0.0058119 | 0.0058348 | 0.5607743 | 0.7488486 |
| ts | mo.1440 | 2018-05-24 | 1440 | 0.0045846 | 0.0045977 | 0.3183663 | 0.5642395 |
| ts | mo.1440 | 2018-05-25 | 1440 | 0.0019628 | 0.0019602 | 0.0623572 | 0.2497142 |
| ts | mo.1440 | 2018-05-26 | 1 | 0.0012225 | 0.0012217 | 0.0178384 | 0.1335606 |
| ts | mo.1440 | 2018-05-28 | 1439 | 0.0007979 | 0.0007973 | 0.0176339 | 0.1327926 |
| ts | mo.1440 | 2018-05-29 | 1440 | 0.0045886 | 0.0046023 | 0.3276230 | 0.5723836 |
| ts | mo.1440 | 2018-05-30 | 1440 | 0.0014840 | 0.0014838 | 0.0348301 | 0.1866283 |
| ts | mo.1440 | 2018-05-31 | 1440 | 0.0013536 | 0.0013549 | 0.0300519 | 0.1733549 |
| ts | mo.1440 | 2018-06-01 | 1440 | 0.0044522 | 0.0044393 | 0.3051694 | 0.5524214 |
| ts | mo.1440 | 2018-06-02 | 1 | 0.0064289 | 0.0064083 | 0.4894299 | 0.6995927 |
| ts | mo.1440 | 2018-06-04 | 1439 | 0.0012318 | 0.0012308 | 0.0252241 | 0.1588209 |
| ts | mo.1440 | 2018-06-05 | 1440 | 0.0008194 | 0.0008192 | 0.0116460 | 0.1079165 |
| ts | mo.1440 | 2018-06-06 | 1440 | 0.0024113 | 0.0024076 | 0.0899958 | 0.2999931 |
| ts | mo.1440 | 2018-06-07 | 1440 | 0.0018578 | 0.0018603 | 0.0608297 | 0.2466369 |
| ts | mo.1440 | 2018-06-08 | 1440 | 0.0015519 | 0.0015535 | 0.0429898 | 0.2073398 |
| ts | mo.1440 | 2018-06-09 | 1 | 0.0015450 | 0.0015462 | 0.0287260 | 0.1694873 |
| ts | mo.1440 | 2018-06-11 | 1439 | 0.0033457 | 0.0033386 | 0.1726245 | 0.4154811 |
| ts | mo.1440 | 2018-06-12 | 1440 | 0.0022748 | 0.0022718 | 0.0723376 | 0.2689565 |
| ts | mo.1440 | 2018-06-13 | 1440 | 0.0013304 | 0.0013291 | 0.0305460 | 0.1747743 |
| ts | mo.1440 | 2018-06-14 | 1440 | 0.0020597 | 0.0020616 | 0.0691778 | 0.2630167 |
| ts | mo.1440 | 2018-06-15 | 1440 | 0.0006625 | 0.0006624 | 0.0085965 | 0.0927175 |
| ts | mo.1440 | 2018-06-16 | 1 | 0.0002951 | 0.0002951 | 0.0010659 | 0.0326477 |
| ts | mo.1440 | 2018-06-18 | 1439 | 0.0013553 | 0.0013564 | 0.0283325 | 0.1683226 |
| ts | mo.1440 | 2018-06-19 | 1440 | 0.0050872 | 0.0051024 | 0.3699783 | 0.6082584 |
| ts | mo.1440 | 2018-06-20 | 1440 | 0.0016517 | 0.0016501 | 0.0409453 | 0.2023495 |
| ts | mo.1440 | 2018-06-21 | 1440 | 0.0023278 | 0.0023273 | 0.0843295 | 0.2903954 |
| ts | mo.1440 | 2018-06-22 | 1440 | 0.0009163 | 0.0009156 | 0.0177474 | 0.1332193 |
| ts | mo.1440 | 2018-06-23 | 1 | 0.0000079 | 0.0000079 | 0.0000008 | 0.0008723 |
| ts | mo.1440 | 2018-06-25 | 1439 | 0.0031281 | 0.0031339 | 0.1395862 | 0.3736124 |
| ts | mo.1440 | 2018-06-26 | 1440 | 0.0014607 | 0.0014593 | 0.0474114 | 0.2177416 |
| ts | mo.1440 | 2018-06-27 | 1440 | 0.0015857 | 0.0015837 | 0.0547408 | 0.2339676 |
| ts | mo.1440 | 2018-06-28 | 1440 | 0.0011801 | 0.0011791 | 0.0260615 | 0.1614359 |
| ts | mo.1440 | 2018-06-29 | 1440 | 0.0022965 | 0.0022933 | 0.0792058 | 0.2814353 |
| ts | mo.1440 | 2018-06-30 | 1 | 0.0017275 | 0.0017260 | 0.0364372 | 0.1908852 |
| ts | mo.1440 | 2018-07-02 | 1439 | 0.0015545 | 0.0015528 | 0.0414666 | 0.2036334 |
| ts | mo.1440 | 2018-07-03 | 1440 | 0.0014015 | 0.0014023 | 0.0366551 | 0.1914552 |
| ts | mo.1440 | 2018-07-04 | 1440 | 0.0006953 | 0.0006956 | 0.0086726 | 0.0931270 |
| ts | mo.1440 | 2018-07-05 | 1440 | 0.0011078 | 0.0011071 | 0.0201046 | 0.1417905 |
| ts | mo.1440 | 2018-07-06 | 1440 | 0.0009011 | 0.0009013 | 0.0152419 | 0.1234581 |
| ts | mo.1440 | 2018-07-07 | 1 | 0.0016363 | 0.0016377 | 0.0327801 | 0.1810527 |
| ts | qt.1440 | 2018-01-03 | 1439 | 0.0006831 | 0.0006827 | 0.0103892 | 0.1019273 |
| ts | qt.1440 | 2018-01-04 | 1440 | 0.0016768 | 0.0016751 | 0.0422922 | 0.2056507 |
| ts | qt.1440 | 2018-01-05 | 1440 | 0.0024953 | 0.0024911 | 0.1075626 | 0.3279673 |
| ts | qt.1440 | 2018-01-06 | 1 | 0.0028290 | 0.0028250 | 0.1017282 | 0.3189485 |
| ts | qt.1440 | 2018-01-08 | 1439 | 0.0007281 | 0.0007278 | 0.0102252 | 0.1011197 |
| ts | qt.1440 | 2018-01-09 | 1440 | 0.0032367 | 0.0032432 | 0.1659303 | 0.4073454 |
| ts | qt.1440 | 2018-01-10 | 1440 | 0.0066417 | 0.0066724 | 0.7752016 | 0.8804553 |
| ts | qt.1440 | 2018-01-11 | 1440 | 0.0021202 | 0.0021179 | 0.0781641 | 0.2795785 |
| ts | qt.1440 | 2018-01-12 | 1440 | 0.0009403 | 0.0009404 | 0.0190289 | 0.1379453 |
| ts | qt.1440 | 2018-01-13 | 1 | 0.0020847 | 0.0020868 | 0.0537916 | 0.2319301 |
| ts | qt.1440 | 2018-01-15 | 1439 | 0.0031809 | 0.0031868 | 0.1450410 | 0.3808425 |
| ts | qt.1440 | 2018-01-16 | 1440 | 0.0019996 | 0.0019972 | 0.0620792 | 0.2491570 |
| ts | qt.1440 | 2018-01-17 | 1440 | 0.0026310 | 0.0026264 | 0.1194394 | 0.3456001 |
| ts | qt.1440 | 2018-01-18 | 1440 | 0.0011188 | 0.0011199 | 0.0305960 | 0.1749171 |
| ts | qt.1440 | 2018-01-19 | 1440 | 0.0032123 | 0.0032183 | 0.1489569 | 0.3859493 |
| ts | qt.1440 | 2018-01-20 | 1 | 0.0025519 | 0.0025552 | 0.0804111 | 0.2835686 |
| ts | qt.1440 | 2018-01-22 | 1439 | 0.0010994 | 0.0010986 | 0.0293561 | 0.1713361 |
| ts | qt.1440 | 2018-01-23 | 1440 | 0.0024651 | 0.0024695 | 0.1109970 | 0.3331621 |
| ts | qt.1440 | 2018-01-24 | 1440 | 0.0056911 | 0.0057129 | 0.5287370 | 0.7271430 |
| ts | qt.1440 | 2018-01-25 | 1440 | 0.0017953 | 0.0017970 | 0.0598675 | 0.2446783 |
| ts | qt.1440 | 2018-01-26 | 1440 | 0.0029656 | 0.0029718 | 0.1737378 | 0.4168187 |
| ts | qt.1440 | 2018-01-27 | 1 | 0.0071425 | 0.0071681 | 0.6106901 | 0.7814666 |
| ts | qt.1440 | 2018-01-29 | 1439 | 0.0026347 | 0.0026295 | 0.1237891 | 0.3518367 |
| ts | qt.1440 | 2018-01-30 | 1440 | 0.0014906 | 0.0014921 | 0.0365624 | 0.1912130 |
| ts | qt.1440 | 2018-01-31 | 1440 | 0.0020757 | 0.0020715 | 0.1017849 | 0.3190375 |
| ts | qt.1440 | 2018-02-01 | 1440 | 0.0027232 | 0.0027180 | 0.1250555 | 0.3536319 |
| ts | qt.1440 | 2018-02-02 | 1440 | 0.0045560 | 0.0045407 | 0.3707291 | 0.6088753 |
| ts | qt.1440 | 2018-02-03 | 1 | 0.0070387 | 0.0070140 | 0.5929877 | 0.7700569 |
| ts | qt.1440 | 2018-02-05 | 1439 | 0.0027180 | 0.0027234 | 0.1321203 | 0.3634836 |
| ts | qt.1440 | 2018-02-06 | 1440 | 0.0019259 | 0.0019271 | 0.0753219 | 0.2744484 |
| ts | qt.1440 | 2018-02-07 | 1440 | 0.0021554 | 0.0021585 | 0.0781449 | 0.2795440 |
| ts | qt.1440 | 2018-02-08 | 1440 | 0.0027445 | 0.0027458 | 0.1333561 | 0.3651796 |
| ts | qt.1440 | 2018-02-09 | 1440 | 0.0020198 | 0.0020201 | 0.0730994 | 0.2703689 |
| ts | qt.1440 | 2018-02-10 | 1 | 0.0003959 | 0.0003958 | 0.0018538 | 0.0430559 |
| ts | qt.1440 | 2018-02-12 | 1439 | 0.0015377 | 0.0015393 | 0.0393168 | 0.1982848 |
| ts | qt.1440 | 2018-02-13 | 1440 | 0.0066809 | 0.0067123 | 0.7424763 | 0.8616707 |
| ts | qt.1440 | 2018-02-14 | 1440 | 0.0047388 | 0.0047535 | 0.3413591 | 0.5842595 |
| ts | qt.1440 | 2018-02-15 | 1440 | 0.0045036 | 0.0045157 | 0.2748755 | 0.5242857 |
| ts | qt.1440 | 2018-02-16 | 1440 | 0.0011753 | 0.0011759 | 0.0262257 | 0.1619436 |
| ts | qt.1440 | 2018-02-17 | 1 | 0.0015951 | 0.0015938 | 0.0286611 | 0.1692959 |
| ts | qt.1440 | 2018-02-19 | 1439 | 0.0023207 | 0.0023174 | 0.0766354 | 0.2768310 |
| ts | qt.1440 | 2018-02-20 | 1440 | 0.0043341 | 0.0043225 | 0.2629109 | 0.5127484 |
| ts | qt.1440 | 2018-02-21 | 1440 | 0.0028600 | 0.0028546 | 0.1260915 | 0.3550936 |
| ts | qt.1440 | 2018-02-22 | 1440 | 0.0051588 | 0.0051765 | 0.4085832 | 0.6392052 |
| ts | qt.1440 | 2018-02-23 | 1440 | 0.0012486 | 0.0012475 | 0.0282839 | 0.1681783 |
| ts | qt.1440 | 2018-02-24 | 1 | 0.0013486 | 0.0013477 | 0.0207232 | 0.1439556 |
| ts | qt.1440 | 2018-02-26 | 1439 | 0.0017962 | 0.0017975 | 0.0481598 | 0.2194533 |
| ts | qt.1440 | 2018-02-27 | 1440 | 0.0020190 | 0.0020153 | 0.0862876 | 0.2937475 |
| ts | qt.1440 | 2018-02-28 | 1440 | 0.0024428 | 0.0024477 | 0.1143788 | 0.3381993 |
| ts | qt.1440 | 2018-03-01 | 1440 | 0.0016694 | 0.0016688 | 0.0470863 | 0.2169937 |
| ts | qt.1440 | 2018-03-02 | 1440 | 0.0048135 | 0.0048289 | 0.3465835 | 0.5887135 |
| ts | qt.1440 | 2018-03-03 | 1 | 0.0047281 | 0.0047393 | 0.2522601 | 0.5022550 |
| ts | qt.1440 | 2018-03-05 | 1439 | 0.0018079 | 0.0018064 | 0.0610287 | 0.2470398 |
| ts | qt.1440 | 2018-03-06 | 1440 | 0.0011802 | 0.0011799 | 0.0240594 | 0.1551111 |
| ts | qt.1440 | 2018-03-07 | 1440 | 0.0029359 | 0.0029414 | 0.1242007 | 0.3524212 |
| ts | qt.1440 | 2018-03-08 | 1440 | 0.0011596 | 0.0011587 | 0.0194579 | 0.1394915 |
| ts | qt.1440 | 2018-03-09 | 1440 | 0.0054740 | 0.0054578 | 0.3673783 | 0.6061174 |
| ts | qt.1440 | 2018-03-10 | 1 | 0.0056414 | 0.0056256 | 0.3591417 | 0.5992843 |
| ts | qt.1440 | 2018-03-12 | 1439 | 0.0021504 | 0.0021533 | 0.0692104 | 0.2630786 |
| ts | qt.1440 | 2018-03-13 | 1440 | 0.0033488 | 0.0033398 | 0.2051598 | 0.4529457 |
| ts | qt.1440 | 2018-03-14 | 1440 | 0.0014264 | 0.0014280 | 0.0381977 | 0.1954424 |
| ts | qt.1440 | 2018-03-15 | 1440 | 0.0023530 | 0.0023566 | 0.0815178 | 0.2855131 |
| ts | qt.1440 | 2018-03-16 | 1440 | 0.0029371 | 0.0029431 | 0.1353705 | 0.3679273 |
| ts | qt.1440 | 2018-03-17 | 1 | 0.0033786 | 0.0033843 | 0.1290836 | 0.3592821 |
| ts | qt.1440 | 2018-03-19 | 1439 | 0.0009708 | 0.0009703 | 0.0165321 | 0.1285770 |
| ts | qt.1440 | 2018-03-20 | 1440 | 0.0026792 | 0.0026749 | 0.0979600 | 0.3129856 |
| ts | qt.1440 | 2018-03-21 | 1440 | 0.0015870 | 0.0015892 | 0.0515675 | 0.2270849 |
| ts | qt.1440 | 2018-03-22 | 1440 | 0.0032348 | 0.0032418 | 0.1569086 | 0.3961169 |
| ts | qt.1440 | 2018-03-23 | 1440 | 0.0029583 | 0.0029635 | 0.1140694 | 0.3377416 |
| ts | qt.1440 | 2018-03-24 | 1 | 0.0051911 | 0.0052046 | 0.2986992 | 0.5465338 |
| ts | qt.1440 | 2018-03-26 | 1439 | 0.0032757 | 0.0032693 | 0.1397978 | 0.3738954 |
| ts | qt.1440 | 2018-03-27 | 1440 | 0.0024380 | 0.0024344 | 0.0789630 | 0.2810036 |
| ts | qt.1440 | 2018-03-28 | 1440 | 0.0053941 | 0.0053695 | 0.5490869 | 0.7410040 |
| ts | qt.1440 | 2018-03-29 | 1440 | 0.0026066 | 0.0026112 | 0.1092411 | 0.3305164 |
| ts | qt.1440 | 2018-03-30 | 1440 | 0.0016551 | 0.0016567 | 0.0378098 | 0.1944474 |
| ts | qt.1440 | 2018-03-31 | 1 | 0.0013389 | 0.0013398 | 0.0203055 | 0.1424974 |
| ts | qt.1440 | 2018-04-02 | 1439 | 0.0015211 | 0.0015227 | 0.0508442 | 0.2254867 |
| ts | qt.1440 | 2018-04-03 | 1440 | 0.0027526 | 0.0027466 | 0.1383391 | 0.3719397 |
| ts | qt.1440 | 2018-04-04 | 1440 | 0.0015243 | 0.0015264 | 0.0539729 | 0.2323207 |
| ts | qt.1440 | 2018-04-05 | 1440 | 0.0034731 | 0.0034652 | 0.1820592 | 0.4266840 |
| ts | qt.1440 | 2018-04-06 | 1440 | 0.0017730 | 0.0017755 | 0.0624358 | 0.2498715 |
| ts | qt.1440 | 2018-04-07 | 1 | 0.0041457 | 0.0041543 | 0.1981815 | 0.4451759 |
| ts | qt.1440 | 2018-04-09 | 1439 | 0.0012110 | 0.0012103 | 0.0239577 | 0.1547826 |
| ts | qt.1440 | 2018-04-10 | 1440 | 0.0027181 | 0.0027134 | 0.1072497 | 0.3274900 |
| ts | qt.1440 | 2018-04-11 | 1440 | 0.0020791 | 0.0020822 | 0.0706898 | 0.2658756 |
| ts | qt.1440 | 2018-04-12 | 1440 | 0.0023507 | 0.0023463 | 0.0995743 | 0.3155540 |
| ts | qt.1440 | 2018-04-13 | 1440 | 0.0014677 | 0.0014659 | 0.0412591 | 0.2031234 |
| ts | qt.1440 | 2018-04-14 | 1 | 0.0003358 | 0.0003358 | 0.0012990 | 0.0360413 |
| ts | qt.1440 | 2018-04-16 | 1439 | 0.0016847 | 0.0016859 | 0.0369616 | 0.1922539 |
| ts | qt.1440 | 2018-04-17 | 1440 | 0.0008862 | 0.0008867 | 0.0128452 | 0.1133366 |
| ts | qt.1440 | 2018-04-18 | 1440 | 0.0018063 | 0.0018042 | 0.0461544 | 0.2148357 |
| ts | qt.1440 | 2018-04-19 | 1440 | 0.0008810 | 0.0008805 | 0.0120259 | 0.1096626 |
| ts | qt.1440 | 2018-04-20 | 1440 | 0.0015958 | 0.0015943 | 0.0358618 | 0.1893721 |
| ts | qt.1440 | 2018-04-21 | 1 | 0.0025518 | 0.0025485 | 0.0750637 | 0.2739776 |
| ts | qt.1440 | 2018-04-23 | 1439 | 0.0040242 | 0.0040104 | 0.3202261 | 0.5658852 |
| ts | qt.1440 | 2018-04-24 | 1440 | 0.0008573 | 0.0008566 | 0.0187051 | 0.1367666 |
| ts | qt.1440 | 2018-04-25 | 1440 | 0.0023128 | 0.0023087 | 0.0965874 | 0.3107851 |
| ts | qt.1440 | 2018-04-26 | 1440 | 0.0013042 | 0.0013054 | 0.0297782 | 0.1725637 |
| ts | qt.1440 | 2018-04-27 | 1440 | 0.0009763 | 0.0009771 | 0.0201485 | 0.1419454 |
| ts | qt.1440 | 2018-04-28 | 1 | 0.0022240 | 0.0022264 | 0.0590888 | 0.2430820 |
| ts | qt.1440 | 2018-04-30 | 1439 | 0.0013332 | 0.0013319 | 0.0303382 | 0.1741787 |
| ts | qt.1440 | 2018-05-01 | 1440 | 0.0018102 | 0.0018076 | 0.0637036 | 0.2523958 |
| ts | qt.1440 | 2018-05-02 | 1440 | 0.0006186 | 0.0006188 | 0.0066917 | 0.0818030 |
| ts | qt.1440 | 2018-05-03 | 1440 | 0.0031580 | 0.0031659 | 0.1898010 | 0.4356616 |
| ts | qt.1440 | 2018-05-04 | 1440 | 0.0008363 | 0.0008369 | 0.0152108 | 0.1233322 |
| ts | qt.1440 | 2018-05-05 | 1 | 0.0010678 | 0.0010684 | 0.0135958 | 0.1166010 |
| ts | qt.1440 | 2018-05-07 | 1439 | 0.0011202 | 0.0011195 | 0.0223646 | 0.1495479 |
| ts | qt.1440 | 2018-05-08 | 1440 | 0.0007796 | 0.0007799 | 0.0113373 | 0.1064767 |
| ts | qt.1440 | 2018-05-09 | 1440 | 0.0043049 | 0.0042941 | 0.2582442 | 0.5081774 |
| ts | qt.1440 | 2018-05-10 | 1440 | 0.0013983 | 0.0013997 | 0.0390225 | 0.1975412 |
| ts | qt.1440 | 2018-05-11 | 1440 | 0.0008717 | 0.0008721 | 0.0130537 | 0.1142527 |
| ts | qt.1440 | 2018-05-12 | 1 | 0.0001088 | 0.0001088 | 0.0001417 | 0.0119035 |
| ts | qt.1440 | 2018-05-14 | 1439 | 0.0009968 | 0.0009961 | 0.0194027 | 0.1392938 |
| ts | qt.1440 | 2018-05-15 | 1440 | 0.0030141 | 0.0030068 | 0.1756007 | 0.4190473 |
| ts | qt.1440 | 2018-05-16 | 1440 | 0.0011822 | 0.0011832 | 0.0246951 | 0.1571468 |
| ts | qt.1440 | 2018-05-17 | 1440 | 0.0020354 | 0.0020327 | 0.0716861 | 0.2677427 |
| ts | qt.1440 | 2018-05-18 | 1440 | 0.0011901 | 0.0011892 | 0.0243190 | 0.1559454 |
| ts | qt.1440 | 2018-05-19 | 1 | 0.0001146 | 0.0001146 | 0.0001610 | 0.0126887 |
| ts | qt.1440 | 2018-05-21 | 1439 | 0.0035854 | 0.0035782 | 0.1766676 | 0.4203184 |
| ts | qt.1440 | 2018-05-22 | 1440 | 0.0010846 | 0.0010854 | 0.0187991 | 0.1371098 |
| ts | qt.1440 | 2018-05-23 | 1440 | 0.0058113 | 0.0058342 | 0.5606810 | 0.7487864 |
| ts | qt.1440 | 2018-05-24 | 1440 | 0.0045846 | 0.0045977 | 0.3183715 | 0.5642442 |
| ts | qt.1440 | 2018-05-25 | 1440 | 0.0019627 | 0.0019601 | 0.0623463 | 0.2496923 |
| ts | qt.1440 | 2018-05-26 | 1 | 0.0012226 | 0.0012218 | 0.0178420 | 0.1335741 |
| ts | qt.1440 | 2018-05-28 | 1439 | 0.0007979 | 0.0007972 | 0.0176343 | 0.1327940 |
| ts | qt.1440 | 2018-05-29 | 1440 | 0.0045874 | 0.0046011 | 0.3274845 | 0.5722627 |
| ts | qt.1440 | 2018-05-30 | 1440 | 0.0014836 | 0.0014834 | 0.0348119 | 0.1865794 |
| ts | qt.1440 | 2018-05-31 | 1440 | 0.0013501 | 0.0013513 | 0.0299007 | 0.1729181 |
| ts | qt.1440 | 2018-06-01 | 1440 | 0.0044538 | 0.0044410 | 0.3054200 | 0.5526482 |
| ts | qt.1440 | 2018-06-02 | 1 | 0.0064294 | 0.0064088 | 0.4895045 | 0.6996460 |
| ts | qt.1440 | 2018-06-04 | 1439 | 0.0012305 | 0.0012295 | 0.0251724 | 0.1586582 |
| ts | qt.1440 | 2018-06-05 | 1440 | 0.0008179 | 0.0008177 | 0.0116054 | 0.1077286 |
| ts | qt.1440 | 2018-06-06 | 1440 | 0.0024067 | 0.0024030 | 0.0897148 | 0.2995243 |
| ts | qt.1440 | 2018-06-07 | 1440 | 0.0018591 | 0.0018616 | 0.0608853 | 0.2467495 |
| ts | qt.1440 | 2018-06-08 | 1440 | 0.0015534 | 0.0015551 | 0.0430697 | 0.2075325 |
| ts | qt.1440 | 2018-06-09 | 1 | 0.0015449 | 0.0015461 | 0.0287242 | 0.1694823 |
| ts | qt.1440 | 2018-06-11 | 1439 | 0.0033475 | 0.0033404 | 0.1728102 | 0.4157044 |
| ts | qt.1440 | 2018-06-12 | 1440 | 0.0022798 | 0.0022768 | 0.0726214 | 0.2694836 |
| ts | qt.1440 | 2018-06-13 | 1440 | 0.0013311 | 0.0013299 | 0.0305674 | 0.1748354 |
| ts | qt.1440 | 2018-06-14 | 1440 | 0.0020601 | 0.0020620 | 0.0692138 | 0.2630851 |
| ts | qt.1440 | 2018-06-15 | 1440 | 0.0006629 | 0.0006627 | 0.0086089 | 0.0927842 |
| ts | qt.1440 | 2018-06-16 | 1 | 0.0002957 | 0.0002957 | 0.0010703 | 0.0327148 |
| ts | qt.1440 | 2018-06-18 | 1439 | 0.0013555 | 0.0013567 | 0.0283448 | 0.1683592 |
| ts | qt.1440 | 2018-06-19 | 1440 | 0.0050862 | 0.0051014 | 0.3698625 | 0.6081632 |
| ts | qt.1440 | 2018-06-20 | 1440 | 0.0016523 | 0.0016506 | 0.0409649 | 0.2023979 |
| ts | qt.1440 | 2018-06-21 | 1440 | 0.0023278 | 0.0023273 | 0.0843434 | 0.2904193 |
| ts | qt.1440 | 2018-06-22 | 1440 | 0.0009162 | 0.0009156 | 0.0177225 | 0.1331258 |
| ts | qt.1440 | 2018-06-23 | 1 | 0.0000088 | 0.0000088 | 0.0000009 | 0.0009659 |
| ts | qt.1440 | 2018-06-25 | 1439 | 0.0031263 | 0.0031321 | 0.1394299 | 0.3734031 |
| ts | qt.1440 | 2018-06-26 | 1440 | 0.0014616 | 0.0014602 | 0.0474650 | 0.2178647 |
| ts | qt.1440 | 2018-06-27 | 1440 | 0.0015873 | 0.0015853 | 0.0548285 | 0.2341548 |
| ts | qt.1440 | 2018-06-28 | 1440 | 0.0011830 | 0.0011820 | 0.0261578 | 0.1617337 |
| ts | qt.1440 | 2018-06-29 | 1440 | 0.0022958 | 0.0022926 | 0.0791540 | 0.2813432 |
| ts | qt.1440 | 2018-06-30 | 1 | 0.0017277 | 0.0017262 | 0.0364452 | 0.1909063 |
| ts | qt.1440 | 2018-07-02 | 1439 | 0.0015529 | 0.0015512 | 0.0413942 | 0.2034557 |
| ts | qt.1440 | 2018-07-03 | 1440 | 0.0014015 | 0.0014022 | 0.0366592 | 0.1914659 |
| ts | qt.1440 | 2018-07-04 | 1440 | 0.0006939 | 0.0006943 | 0.0086466 | 0.0929872 |
| ts | qt.1440 | 2018-07-05 | 1440 | 0.0011100 | 0.0011093 | 0.0201886 | 0.1420867 |
| ts | qt.1440 | 2018-07-06 | 1440 | 0.0009011 | 0.0009014 | 0.0151943 | 0.1232651 |
| ts | qt.1440 | 2018-07-07 | 1 | 0.0016328 | 0.0016341 | 0.0326368 | 0.1806567 |
| ts | wk.1440 | 2018-01-03 | 1439 | 0.0006377 | 0.0006374 | 0.0093590 | 0.0967421 |
| ts | wk.1440 | 2018-01-04 | 1440 | 0.0015429 | 0.0015414 | 0.0365370 | 0.1911465 |
| ts | wk.1440 | 2018-01-05 | 1440 | 0.0024296 | 0.0024257 | 0.1005683 | 0.3171250 |
| ts | wk.1440 | 2018-01-06 | 1 | 0.0027088 | 0.0027051 | 0.0932913 | 0.3054363 |
| ts | wk.1440 | 2018-01-08 | 1439 | 0.0007430 | 0.0007427 | 0.0116784 | 0.1080667 |
| ts | wk.1440 | 2018-01-09 | 1440 | 0.0034737 | 0.0034810 | 0.1879770 | 0.4335632 |
| ts | wk.1440 | 2018-01-10 | 1440 | 0.0068096 | 0.0068410 | 0.7921221 | 0.8900124 |
| ts | wk.1440 | 2018-01-11 | 1440 | 0.0022222 | 0.0022198 | 0.0813264 | 0.2851778 |
| ts | wk.1440 | 2018-01-12 | 1440 | 0.0010002 | 0.0010003 | 0.0205997 | 0.1435259 |
| ts | wk.1440 | 2018-01-13 | 1 | 0.0020481 | 0.0020502 | 0.0519180 | 0.2278553 |
| ts | wk.1440 | 2018-01-15 | 1439 | 0.0033845 | 0.0033910 | 0.1606568 | 0.4008201 |
| ts | wk.1440 | 2018-01-16 | 1440 | 0.0038929 | 0.0038844 | 0.2090785 | 0.4572511 |
| ts | wk.1440 | 2018-01-17 | 1440 | 0.0021212 | 0.0021181 | 0.0928568 | 0.3047242 |
| ts | wk.1440 | 2018-01-18 | 1440 | 0.0013063 | 0.0013076 | 0.0382794 | 0.1956513 |
| ts | wk.1440 | 2018-01-19 | 1440 | 0.0031640 | 0.0031700 | 0.1464485 | 0.3826859 |
| ts | wk.1440 | 2018-01-20 | 1 | 0.0024653 | 0.0024684 | 0.0750321 | 0.2739199 |
| ts | wk.1440 | 2018-01-22 | 1439 | 0.0012033 | 0.0012022 | 0.0367588 | 0.1917259 |
| ts | wk.1440 | 2018-01-23 | 1440 | 0.0023469 | 0.0023505 | 0.0954409 | 0.3089351 |
| ts | wk.1440 | 2018-01-24 | 1440 | 0.0053082 | 0.0053277 | 0.4719133 | 0.6869595 |
| ts | wk.1440 | 2018-01-25 | 1440 | 0.0015920 | 0.0015935 | 0.0514737 | 0.2268782 |
| ts | wk.1440 | 2018-01-26 | 1440 | 0.0028989 | 0.0029047 | 0.1639420 | 0.4048975 |
| ts | wk.1440 | 2018-01-27 | 1 | 0.0071927 | 0.0072187 | 0.6193685 | 0.7869997 |
| ts | wk.1440 | 2018-01-29 | 1439 | 0.0025037 | 0.0024987 | 0.1234091 | 0.3512963 |
| ts | wk.1440 | 2018-01-30 | 1440 | 0.0019092 | 0.0019114 | 0.0563017 | 0.2372798 |
| ts | wk.1440 | 2018-01-31 | 1440 | 0.0020460 | 0.0020419 | 0.1019659 | 0.3193210 |
| ts | wk.1440 | 2018-02-01 | 1440 | 0.0026329 | 0.0026280 | 0.1186766 | 0.3444947 |
| ts | wk.1440 | 2018-02-02 | 1440 | 0.0041788 | 0.0041658 | 0.3134566 | 0.5598719 |
| ts | wk.1440 | 2018-02-03 | 1 | 0.0071070 | 0.0070818 | 0.6044744 | 0.7774795 |
| ts | wk.1440 | 2018-02-05 | 1439 | 0.0028535 | 0.0028594 | 0.1418618 | 0.3766454 |
| ts | wk.1440 | 2018-02-06 | 1440 | 0.0019690 | 0.0019706 | 0.0768099 | 0.2771461 |
| ts | wk.1440 | 2018-02-07 | 1440 | 0.0023334 | 0.0023370 | 0.0921589 | 0.3035769 |
| ts | wk.1440 | 2018-02-08 | 1440 | 0.0030423 | 0.0030433 | 0.1522833 | 0.3902349 |
| ts | wk.1440 | 2018-02-09 | 1440 | 0.0021768 | 0.0021772 | 0.0792454 | 0.2815057 |
| ts | wk.1440 | 2018-02-10 | 1 | 0.0004803 | 0.0004802 | 0.0027276 | 0.0522260 |
| ts | wk.1440 | 2018-02-12 | 1439 | 0.0017020 | 0.0017041 | 0.0513134 | 0.2265246 |
| ts | wk.1440 | 2018-02-13 | 1440 | 0.0064973 | 0.0065272 | 0.7033481 | 0.8386585 |
| ts | wk.1440 | 2018-02-14 | 1440 | 0.0046830 | 0.0046971 | 0.3265691 | 0.5714622 |
| ts | wk.1440 | 2018-02-15 | 1440 | 0.0044289 | 0.0044405 | 0.2648426 | 0.5146286 |
| ts | wk.1440 | 2018-02-16 | 1440 | 0.0013118 | 0.0013117 | 0.0283733 | 0.1684438 |
| ts | wk.1440 | 2018-02-17 | 1 | 0.0016105 | 0.0016092 | 0.0292167 | 0.1709288 |
| ts | wk.1440 | 2018-02-19 | 1439 | 0.0028652 | 0.0028601 | 0.1188276 | 0.3447138 |
| ts | wk.1440 | 2018-02-20 | 1440 | 0.0043710 | 0.0043593 | 0.2672058 | 0.5169196 |
| ts | wk.1440 | 2018-02-21 | 1440 | 0.0026410 | 0.0026358 | 0.1206757 | 0.3473841 |
| ts | wk.1440 | 2018-02-22 | 1440 | 0.0054411 | 0.0054605 | 0.4496075 | 0.6705278 |
| ts | wk.1440 | 2018-02-23 | 1440 | 0.0010505 | 0.0010499 | 0.0189255 | 0.1375698 |
| ts | wk.1440 | 2018-02-24 | 1 | 0.0012833 | 0.0012825 | 0.0187693 | 0.1370010 |
| ts | wk.1440 | 2018-02-26 | 1439 | 0.0021052 | 0.0021071 | 0.0690037 | 0.2626856 |
| ts | wk.1440 | 2018-02-27 | 1440 | 0.0021804 | 0.0021763 | 0.0961102 | 0.3100165 |
| ts | wk.1440 | 2018-02-28 | 1440 | 0.0024000 | 0.0024050 | 0.1150795 | 0.3392337 |
| ts | wk.1440 | 2018-03-01 | 1440 | 0.0016842 | 0.0016839 | 0.0462265 | 0.2150035 |
| ts | wk.1440 | 2018-03-02 | 1440 | 0.0051332 | 0.0051505 | 0.3896439 | 0.6242147 |
| ts | wk.1440 | 2018-03-03 | 1 | 0.0047451 | 0.0047564 | 0.2540904 | 0.5040738 |
| ts | wk.1440 | 2018-03-05 | 1439 | 0.0015891 | 0.0015877 | 0.0514395 | 0.2268027 |
| ts | wk.1440 | 2018-03-06 | 1440 | 0.0013126 | 0.0013123 | 0.0280608 | 0.1675135 |
| ts | wk.1440 | 2018-03-07 | 1440 | 0.0030734 | 0.0030794 | 0.1349351 | 0.3673351 |
| ts | wk.1440 | 2018-03-08 | 1440 | 0.0016855 | 0.0016838 | 0.0379365 | 0.1947730 |
| ts | wk.1440 | 2018-03-09 | 1440 | 0.0061676 | 0.0061470 | 0.4652995 | 0.6821286 |
| ts | wk.1440 | 2018-03-10 | 1 | 0.0057299 | 0.0057136 | 0.3704323 | 0.6086315 |
| ts | wk.1440 | 2018-03-12 | 1439 | 0.0020176 | 0.0020203 | 0.0628140 | 0.2506272 |
| ts | wk.1440 | 2018-03-13 | 1440 | 0.0033350 | 0.0033267 | 0.1935115 | 0.4398994 |
| ts | wk.1440 | 2018-03-14 | 1440 | 0.0020142 | 0.0020168 | 0.0584872 | 0.2418413 |
| ts | wk.1440 | 2018-03-15 | 1440 | 0.0029342 | 0.0029399 | 0.1304239 | 0.3611425 |
| ts | wk.1440 | 2018-03-16 | 1440 | 0.0030449 | 0.0030515 | 0.1517832 | 0.3895936 |
| ts | wk.1440 | 2018-03-17 | 1 | 0.0033993 | 0.0034051 | 0.1306823 | 0.3615000 |
| ts | wk.1440 | 2018-03-19 | 1439 | 0.0009585 | 0.0009582 | 0.0168920 | 0.1299693 |
| ts | wk.1440 | 2018-03-20 | 1440 | 0.0030837 | 0.0030779 | 0.1289772 | 0.3591340 |
| ts | wk.1440 | 2018-03-21 | 1440 | 0.0013897 | 0.0013913 | 0.0415519 | 0.2038428 |
| ts | wk.1440 | 2018-03-22 | 1440 | 0.0030439 | 0.0030502 | 0.1406609 | 0.3750479 |
| ts | wk.1440 | 2018-03-23 | 1440 | 0.0032527 | 0.0032589 | 0.1361459 | 0.3689795 |
| ts | wk.1440 | 2018-03-24 | 1 | 0.0051860 | 0.0051995 | 0.2981044 | 0.5459894 |
| ts | wk.1440 | 2018-03-26 | 1439 | 0.0029438 | 0.0029386 | 0.1147257 | 0.3387119 |
| ts | wk.1440 | 2018-03-27 | 1440 | 0.0022064 | 0.0022034 | 0.0655104 | 0.2559499 |
| ts | wk.1440 | 2018-03-28 | 1440 | 0.0045837 | 0.0045633 | 0.4556683 | 0.6750321 |
| ts | wk.1440 | 2018-03-29 | 1440 | 0.0027442 | 0.0027492 | 0.1195169 | 0.3457122 |
| ts | wk.1440 | 2018-03-30 | 1440 | 0.0016119 | 0.0016134 | 0.0364448 | 0.1909051 |
| ts | wk.1440 | 2018-03-31 | 1 | 0.0013532 | 0.0013541 | 0.0207428 | 0.1440237 |
| ts | wk.1440 | 2018-04-02 | 1439 | 0.0017560 | 0.0017569 | 0.0529399 | 0.2300868 |
| ts | wk.1440 | 2018-04-03 | 1440 | 0.0029711 | 0.0029644 | 0.1556651 | 0.3945441 |
| ts | wk.1440 | 2018-04-04 | 1440 | 0.0014267 | 0.0014281 | 0.0418298 | 0.2045232 |
| ts | wk.1440 | 2018-04-05 | 1440 | 0.0036514 | 0.0036426 | 0.2012721 | 0.4486336 |
| ts | wk.1440 | 2018-04-06 | 1440 | 0.0017782 | 0.0017806 | 0.0612359 | 0.2474589 |
| ts | wk.1440 | 2018-04-07 | 1 | 0.0041445 | 0.0041532 | 0.1980730 | 0.4450539 |
| ts | wk.1440 | 2018-04-09 | 1439 | 0.0012175 | 0.0012169 | 0.0232286 | 0.1524094 |
| ts | wk.1440 | 2018-04-10 | 1440 | 0.0026957 | 0.0026912 | 0.1033647 | 0.3215037 |
| ts | wk.1440 | 2018-04-11 | 1440 | 0.0023617 | 0.0023654 | 0.0863748 | 0.2938960 |
| ts | wk.1440 | 2018-04-12 | 1440 | 0.0020443 | 0.0020406 | 0.0837986 | 0.2894799 |
| ts | wk.1440 | 2018-04-13 | 1440 | 0.0011664 | 0.0011652 | 0.0263757 | 0.1624061 |
| ts | wk.1440 | 2018-04-14 | 1 | 0.0003228 | 0.0003228 | 0.0012002 | 0.0346437 |
| ts | wk.1440 | 2018-04-16 | 1439 | 0.0018894 | 0.0018910 | 0.0464018 | 0.2154108 |
| ts | wk.1440 | 2018-04-17 | 1440 | 0.0008097 | 0.0008102 | 0.0106438 | 0.1031689 |
| ts | wk.1440 | 2018-04-18 | 1440 | 0.0018186 | 0.0018165 | 0.0497680 | 0.2230875 |
| ts | wk.1440 | 2018-04-19 | 1440 | 0.0008881 | 0.0008876 | 0.0120401 | 0.1097273 |
| ts | wk.1440 | 2018-04-20 | 1440 | 0.0014749 | 0.0014735 | 0.0321726 | 0.1793671 |
| ts | wk.1440 | 2018-04-21 | 1 | 0.0025507 | 0.0025474 | 0.0750001 | 0.2738615 |
| ts | wk.1440 | 2018-04-23 | 1439 | 0.0039410 | 0.0039272 | 0.3221683 | 0.5675987 |
| ts | wk.1440 | 2018-04-24 | 1440 | 0.0026305 | 0.0026357 | 0.1272682 | 0.3567467 |
| ts | wk.1440 | 2018-04-25 | 1440 | 0.0009388 | 0.0009382 | 0.0165561 | 0.1286705 |
| ts | wk.1440 | 2018-04-26 | 1440 | 0.0032163 | 0.0032232 | 0.1669224 | 0.4085613 |
| ts | wk.1440 | 2018-04-27 | 1440 | 0.0010050 | 0.0010055 | 0.0190342 | 0.1379645 |
| ts | wk.1440 | 2018-04-28 | 1 | 0.0022235 | 0.0022260 | 0.0590657 | 0.2430344 |
| ts | wk.1440 | 2018-04-30 | 1439 | 0.0016206 | 0.0016189 | 0.0404867 | 0.2012132 |
| ts | wk.1440 | 2018-05-01 | 1440 | 0.0018381 | 0.0018354 | 0.0667639 | 0.2583872 |
| ts | wk.1440 | 2018-05-02 | 1440 | 0.0005955 | 0.0005955 | 0.0058934 | 0.0767684 |
| ts | wk.1440 | 2018-05-03 | 1440 | 0.0031220 | 0.0031297 | 0.1873461 | 0.4328349 |
| ts | wk.1440 | 2018-05-04 | 1440 | 0.0008457 | 0.0008463 | 0.0155368 | 0.1246468 |
| ts | wk.1440 | 2018-05-05 | 1 | 0.0010686 | 0.0010692 | 0.0136154 | 0.1166849 |
| ts | wk.1440 | 2018-05-07 | 1439 | 0.0012400 | 0.0012390 | 0.0274047 | 0.1655437 |
| ts | wk.1440 | 2018-05-08 | 1440 | 0.0008154 | 0.0008157 | 0.0122286 | 0.1105829 |
| ts | wk.1440 | 2018-05-09 | 1440 | 0.0042896 | 0.0042790 | 0.2543471 | 0.5043284 |
| ts | wk.1440 | 2018-05-10 | 1440 | 0.0015154 | 0.0015171 | 0.0451042 | 0.2123774 |
| ts | wk.1440 | 2018-05-11 | 1440 | 0.0010083 | 0.0010090 | 0.0184580 | 0.1358603 |
| ts | wk.1440 | 2018-05-12 | 1 | 0.0001095 | 0.0001095 | 0.0001434 | 0.0119770 |
| ts | wk.1440 | 2018-05-14 | 1439 | 0.0009805 | 0.0009799 | 0.0189849 | 0.1377855 |
| ts | wk.1440 | 2018-05-15 | 1440 | 0.0029573 | 0.0029500 | 0.1769324 | 0.4206334 |
| ts | wk.1440 | 2018-05-16 | 1440 | 0.0011120 | 0.0011129 | 0.0215632 | 0.1468440 |
| ts | wk.1440 | 2018-05-17 | 1440 | 0.0022316 | 0.0022281 | 0.0887804 | 0.2979604 |
| ts | wk.1440 | 2018-05-18 | 1440 | 0.0015236 | 0.0015220 | 0.0400530 | 0.2001325 |
| ts | wk.1440 | 2018-05-19 | 1 | 0.0001146 | 0.0001146 | 0.0001611 | 0.0126929 |
| ts | wk.1440 | 2018-05-21 | 1439 | 0.0037959 | 0.0037878 | 0.1992589 | 0.4463843 |
| ts | wk.1440 | 2018-05-22 | 1440 | 0.0012439 | 0.0012449 | 0.0245710 | 0.1567513 |
| ts | wk.1440 | 2018-05-23 | 1440 | 0.0060539 | 0.0060785 | 0.6027881 | 0.7763943 |
| ts | wk.1440 | 2018-05-24 | 1440 | 0.0046682 | 0.0046817 | 0.3281552 | 0.5728483 |
| ts | wk.1440 | 2018-05-25 | 1440 | 0.0019685 | 0.0019659 | 0.0621719 | 0.2493430 |
| ts | wk.1440 | 2018-05-26 | 1 | 0.0012220 | 0.0012213 | 0.0178259 | 0.1335135 |
| ts | wk.1440 | 2018-05-28 | 1439 | 0.0008636 | 0.0008628 | 0.0196285 | 0.1401017 |
| ts | wk.1440 | 2018-05-29 | 1440 | 0.0045162 | 0.0045295 | 0.3155873 | 0.5617716 |
| ts | wk.1440 | 2018-05-30 | 1440 | 0.0017530 | 0.0017527 | 0.0479193 | 0.2189048 |
| ts | wk.1440 | 2018-05-31 | 1440 | 0.0015136 | 0.0015151 | 0.0356393 | 0.1887837 |
| ts | wk.1440 | 2018-06-01 | 1440 | 0.0046222 | 0.0046085 | 0.3254560 | 0.5704875 |
| ts | wk.1440 | 2018-06-02 | 1 | 0.0064294 | 0.0064088 | 0.4895020 | 0.6996442 |
| ts | wk.1440 | 2018-06-04 | 1439 | 0.0014075 | 0.0014062 | 0.0326237 | 0.1806204 |
| ts | wk.1440 | 2018-06-05 | 1440 | 0.0009757 | 0.0009754 | 0.0164131 | 0.1281135 |
| ts | wk.1440 | 2018-06-06 | 1440 | 0.0023960 | 0.0023925 | 0.0853821 | 0.2922022 |
| ts | wk.1440 | 2018-06-07 | 1440 | 0.0020312 | 0.0020341 | 0.0696411 | 0.2638960 |
| ts | wk.1440 | 2018-06-08 | 1440 | 0.0015560 | 0.0015578 | 0.0447179 | 0.2114662 |
| ts | wk.1440 | 2018-06-09 | 1 | 0.0015441 | 0.0015453 | 0.0286927 | 0.1693892 |
| ts | wk.1440 | 2018-06-11 | 1439 | 0.0034839 | 0.0034765 | 0.1822737 | 0.4269352 |
| ts | wk.1440 | 2018-06-12 | 1440 | 0.0020918 | 0.0020893 | 0.0621825 | 0.2493641 |
| ts | wk.1440 | 2018-06-13 | 1440 | 0.0012377 | 0.0012366 | 0.0270009 | 0.1643196 |
| ts | wk.1440 | 2018-06-14 | 1440 | 0.0022918 | 0.0022947 | 0.0869863 | 0.2949344 |
| ts | wk.1440 | 2018-06-15 | 1440 | 0.0007416 | 0.0007414 | 0.0109773 | 0.1047727 |
| ts | wk.1440 | 2018-06-16 | 1 | 0.0002949 | 0.0002948 | 0.0010641 | 0.0326204 |
| ts | wk.1440 | 2018-06-18 | 1439 | 0.0012722 | 0.0012732 | 0.0261586 | 0.1617362 |
| ts | wk.1440 | 2018-06-19 | 1440 | 0.0047863 | 0.0047996 | 0.3251664 | 0.5702337 |
| ts | wk.1440 | 2018-06-20 | 1440 | 0.0024198 | 0.0024165 | 0.0794441 | 0.2818583 |
| ts | wk.1440 | 2018-06-21 | 1440 | 0.0026895 | 0.0026874 | 0.1111407 | 0.3333777 |
| ts | wk.1440 | 2018-06-22 | 1440 | 0.0009687 | 0.0009681 | 0.0174531 | 0.1321104 |
| ts | wk.1440 | 2018-06-23 | 1 | 0.0000103 | 0.0000103 | 0.0000013 | 0.0011338 |
| ts | wk.1440 | 2018-06-25 | 1439 | 0.0033070 | 0.0033133 | 0.1539469 | 0.3923607 |
| ts | wk.1440 | 2018-06-26 | 1440 | 0.0015940 | 0.0015926 | 0.0536322 | 0.2315862 |
| ts | wk.1440 | 2018-06-27 | 1440 | 0.0016759 | 0.0016741 | 0.0551545 | 0.2348499 |
| ts | wk.1440 | 2018-06-28 | 1440 | 0.0012185 | 0.0012175 | 0.0273435 | 0.1653586 |
| ts | wk.1440 | 2018-06-29 | 1440 | 0.0026798 | 0.0026757 | 0.1016952 | 0.3188969 |
| ts | wk.1440 | 2018-06-30 | 1 | 0.0017275 | 0.0017260 | 0.0364363 | 0.1908830 |
| ts | wk.1440 | 2018-07-02 | 1439 | 0.0016023 | 0.0016004 | 0.0462015 | 0.2149454 |
| ts | wk.1440 | 2018-07-03 | 1440 | 0.0015382 | 0.0015392 | 0.0459171 | 0.2142827 |
| ts | wk.1440 | 2018-07-04 | 1440 | 0.0010481 | 0.0010488 | 0.0180869 | 0.1344874 |
| ts | wk.1440 | 2018-07-05 | 1440 | 0.0010587 | 0.0010582 | 0.0168149 | 0.1296722 |
| ts | wk.1440 | 2018-07-06 | 1440 | 0.0008894 | 0.0008899 | 0.0144213 | 0.1200889 |
| ts | wk.1440 | 2018-07-07 | 1 | 0.0016397 | 0.0016410 | 0.0329140 | 0.1814223 |
| ts | wk.7200 | 2018-01-03 | 7195 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| ts | wk.7200 | 2018-01-04 | 7200 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| ts | wk.7200 | 2018-01-05 | 7200 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| ts | wk.7200 | 2018-01-06 | 5 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| ts | wk.7200 | 2018-01-08 | 7195 | 0.0039391 | 0.0039311 | 0.2050746 | 0.4528517 |
| ts | wk.7200 | 2018-01-09 | 7200 | 0.0040211 | 0.0040307 | 0.2464068 | 0.4963938 |
| ts | wk.7200 | 2018-01-10 | 7200 | 0.0070906 | 0.0071240 | 0.8446258 | 0.9190353 |
| ts | wk.7200 | 2018-01-11 | 7200 | 0.0016810 | 0.0016802 | 0.0501111 | 0.2238550 |
| ts | wk.7200 | 2018-01-12 | 7200 | 0.0009459 | 0.0009462 | 0.0193830 | 0.1392229 |
| ts | wk.7200 | 2018-01-13 | 5 | 0.0020951 | 0.0020973 | 0.0543298 | 0.2330875 |
| ts | wk.7200 | 2018-01-15 | 7195 | 0.0032362 | 0.0032424 | 0.1531036 | 0.3912845 |
| ts | wk.7200 | 2018-01-16 | 7200 | 0.0018546 | 0.0018528 | 0.0537027 | 0.2317384 |
| ts | wk.7200 | 2018-01-17 | 7200 | 0.0026467 | 0.0026420 | 0.1168366 | 0.3418137 |
| ts | wk.7200 | 2018-01-18 | 7200 | 0.0012101 | 0.0012114 | 0.0359617 | 0.1896357 |
| ts | wk.7200 | 2018-01-19 | 7200 | 0.0030660 | 0.0030718 | 0.1439754 | 0.3794408 |
| ts | wk.7200 | 2018-01-20 | 5 | 0.0024655 | 0.0024686 | 0.0750439 | 0.2739413 |
| ts | wk.7200 | 2018-01-22 | 7195 | 0.0009303 | 0.0009301 | 0.0176592 | 0.1328879 |
| ts | wk.7200 | 2018-01-23 | 7200 | 0.0027056 | 0.0027112 | 0.1388723 | 0.3726558 |
| ts | wk.7200 | 2018-01-24 | 7200 | 0.0059676 | 0.0059923 | 0.6004224 | 0.7748693 |
| ts | wk.7200 | 2018-01-25 | 7200 | 0.0021473 | 0.0021505 | 0.0859483 | 0.2931694 |
| ts | wk.7200 | 2018-01-26 | 7200 | 0.0035808 | 0.0035912 | 0.2610875 | 0.5109672 |
| ts | wk.7200 | 2018-01-27 | 5 | 0.0071927 | 0.0072187 | 0.6193681 | 0.7869994 |
| ts | wk.7200 | 2018-01-29 | 7195 | 0.0020564 | 0.0020535 | 0.0690661 | 0.2628043 |
| ts | wk.7200 | 2018-01-30 | 7200 | 0.0017880 | 0.0017901 | 0.0518208 | 0.2276417 |
| ts | wk.7200 | 2018-01-31 | 7200 | 0.0015933 | 0.0015908 | 0.0616236 | 0.2482410 |
| ts | wk.7200 | 2018-02-01 | 7200 | 0.0021347 | 0.0021316 | 0.0759614 | 0.2756109 |
| ts | wk.7200 | 2018-02-02 | 7200 | 0.0043702 | 0.0043564 | 0.3327274 | 0.5768253 |
| ts | wk.7200 | 2018-02-03 | 5 | 0.0071064 | 0.0070813 | 0.6043809 | 0.7774194 |
| ts | wk.7200 | 2018-02-05 | 7195 | 0.0026141 | 0.0026193 | 0.1267205 | 0.3559782 |
| ts | wk.7200 | 2018-02-06 | 7200 | 0.0019374 | 0.0019371 | 0.0695778 | 0.2637761 |
| ts | wk.7200 | 2018-02-07 | 7200 | 0.0023371 | 0.0023408 | 0.0920698 | 0.3034301 |
| ts | wk.7200 | 2018-02-08 | 7200 | 0.0024018 | 0.0024023 | 0.1001011 | 0.3163876 |
| ts | wk.7200 | 2018-02-09 | 7200 | 0.0019889 | 0.0019878 | 0.0677661 | 0.2603193 |
| ts | wk.7200 | 2018-02-10 | 5 | 0.0004745 | 0.0004744 | 0.0026630 | 0.0516045 |
| ts | wk.7200 | 2018-02-12 | 7195 | 0.0011758 | 0.0011766 | 0.0200692 | 0.1416658 |
| ts | wk.7200 | 2018-02-13 | 7200 | 0.0061931 | 0.0062203 | 0.6398331 | 0.7998957 |
| ts | wk.7200 | 2018-02-14 | 7200 | 0.0049931 | 0.0050091 | 0.3708889 | 0.6090065 |
| ts | wk.7200 | 2018-02-15 | 7200 | 0.0047551 | 0.0047683 | 0.3013010 | 0.5489089 |
| ts | wk.7200 | 2018-02-16 | 7200 | 0.0013685 | 0.0013695 | 0.0367189 | 0.1916218 |
| ts | wk.7200 | 2018-02-17 | 5 | 0.0016104 | 0.0016091 | 0.0292141 | 0.1709214 |
| ts | wk.7200 | 2018-02-19 | 7195 | 0.0018805 | 0.0018784 | 0.0502624 | 0.2241928 |
| ts | wk.7200 | 2018-02-20 | 7200 | 0.0039183 | 0.0039084 | 0.2261113 | 0.4755116 |
| ts | wk.7200 | 2018-02-21 | 7200 | 0.0025421 | 0.0025380 | 0.0954939 | 0.3090209 |
| ts | wk.7200 | 2018-02-22 | 7200 | 0.0053752 | 0.0053940 | 0.4360534 | 0.6603434 |
| ts | wk.7200 | 2018-02-23 | 7200 | 0.0010670 | 0.0010664 | 0.0194058 | 0.1393048 |
| ts | wk.7200 | 2018-02-24 | 5 | 0.0012833 | 0.0012825 | 0.0187690 | 0.1370001 |
| ts | wk.7200 | 2018-02-26 | 7195 | 0.0017220 | 0.0017237 | 0.0488638 | 0.2210516 |
| ts | wk.7200 | 2018-02-27 | 7200 | 0.0017670 | 0.0017641 | 0.0695035 | 0.2636352 |
| ts | wk.7200 | 2018-02-28 | 7200 | 0.0028541 | 0.0028601 | 0.1382651 | 0.3718401 |
| ts | wk.7200 | 2018-03-01 | 7200 | 0.0014271 | 0.0014270 | 0.0407566 | 0.2018827 |
| ts | wk.7200 | 2018-03-02 | 7200 | 0.0044549 | 0.0044685 | 0.3069355 | 0.5540176 |
| ts | wk.7200 | 2018-03-03 | 5 | 0.0047465 | 0.0047578 | 0.2542408 | 0.5042230 |
| ts | wk.7200 | 2018-03-05 | 7195 | 0.0020813 | 0.0020805 | 0.0656674 | 0.2562564 |
| ts | wk.7200 | 2018-03-06 | 7200 | 0.0010509 | 0.0010512 | 0.0191604 | 0.1384211 |
| ts | wk.7200 | 2018-03-07 | 7200 | 0.0032838 | 0.0032906 | 0.1519187 | 0.3897674 |
| ts | wk.7200 | 2018-03-08 | 7200 | 0.0006008 | 0.0006007 | 0.0064412 | 0.0802574 |
| ts | wk.7200 | 2018-03-09 | 7200 | 0.0048046 | 0.0047919 | 0.2882735 | 0.5369110 |
| ts | wk.7200 | 2018-03-10 | 5 | 0.0057323 | 0.0057160 | 0.3707428 | 0.6088865 |
| ts | wk.7200 | 2018-03-12 | 7195 | 0.0023398 | 0.0023430 | 0.0759610 | 0.2756102 |
| ts | wk.7200 | 2018-03-13 | 7200 | 0.0028998 | 0.0028929 | 0.1571938 | 0.3964767 |
| ts | wk.7200 | 2018-03-14 | 7200 | 0.0013293 | 0.0013307 | 0.0331116 | 0.1819659 |
| ts | wk.7200 | 2018-03-15 | 7200 | 0.0023837 | 0.0023874 | 0.0828075 | 0.2877628 |
| ts | wk.7200 | 2018-03-16 | 7200 | 0.0033265 | 0.0033339 | 0.1664579 | 0.4079925 |
| ts | wk.7200 | 2018-03-17 | 5 | 0.0033993 | 0.0034051 | 0.1306823 | 0.3615000 |
| ts | wk.7200 | 2018-03-19 | 7195 | 0.0011848 | 0.0011850 | 0.0217902 | 0.1476151 |
| ts | wk.7200 | 2018-03-20 | 7200 | 0.0022842 | 0.0022809 | 0.0756470 | 0.2750400 |
| ts | wk.7200 | 2018-03-21 | 7200 | 0.0017213 | 0.0017238 | 0.0554275 | 0.2354305 |
| ts | wk.7200 | 2018-03-22 | 7200 | 0.0034457 | 0.0034532 | 0.1688587 | 0.4109242 |
| ts | wk.7200 | 2018-03-23 | 7200 | 0.0032288 | 0.0032349 | 0.1359440 | 0.3687058 |
| ts | wk.7200 | 2018-03-24 | 5 | 0.0051860 | 0.0051995 | 0.2981042 | 0.5459892 |
| ts | wk.7200 | 2018-03-26 | 7195 | 0.0028857 | 0.0028803 | 0.1198486 | 0.3461916 |
| ts | wk.7200 | 2018-03-27 | 7200 | 0.0019739 | 0.0019715 | 0.0548889 | 0.2342838 |
| ts | wk.7200 | 2018-03-28 | 7200 | 0.0054905 | 0.0054644 | 0.5832838 | 0.7637302 |
| ts | wk.7200 | 2018-03-29 | 7200 | 0.0026980 | 0.0027026 | 0.1069103 | 0.3269714 |
| ts | wk.7200 | 2018-03-30 | 7200 | 0.0017344 | 0.0017361 | 0.0397622 | 0.1994047 |
| ts | wk.7200 | 2018-03-31 | 5 | 0.0013530 | 0.0013539 | 0.0207364 | 0.1440013 |
| ts | wk.7200 | 2018-04-02 | 7195 | 0.0011295 | 0.0011310 | 0.0377658 | 0.1943343 |
| ts | wk.7200 | 2018-04-03 | 7200 | 0.0027909 | 0.0027843 | 0.1512558 | 0.3889162 |
| ts | wk.7200 | 2018-04-04 | 7200 | 0.0017285 | 0.0017308 | 0.0600590 | 0.2450693 |
| ts | wk.7200 | 2018-04-05 | 7200 | 0.0028601 | 0.0028538 | 0.1440498 | 0.3795390 |
| ts | wk.7200 | 2018-04-06 | 7200 | 0.0017681 | 0.0017708 | 0.0637109 | 0.2524102 |
| ts | wk.7200 | 2018-04-07 | 5 | 0.0041453 | 0.0041539 | 0.1981415 | 0.4451308 |
| ts | wk.7200 | 2018-04-09 | 7195 | 0.0009029 | 0.0009026 | 0.0139964 | 0.1183064 |
| ts | wk.7200 | 2018-04-10 | 7200 | 0.0026414 | 0.0026370 | 0.1022637 | 0.3197870 |
| ts | wk.7200 | 2018-04-11 | 7200 | 0.0020889 | 0.0020919 | 0.0689249 | 0.2625356 |
| ts | wk.7200 | 2018-04-12 | 7200 | 0.0022912 | 0.0022869 | 0.0980558 | 0.3131386 |
| ts | wk.7200 | 2018-04-13 | 7200 | 0.0015215 | 0.0015197 | 0.0421425 | 0.2052864 |
| ts | wk.7200 | 2018-04-14 | 5 | 0.0003216 | 0.0003215 | 0.0011909 | 0.0345098 |
| ts | wk.7200 | 2018-04-16 | 7195 | 0.0012819 | 0.0012826 | 0.0235916 | 0.1535956 |
| ts | wk.7200 | 2018-04-17 | 7200 | 0.0006962 | 0.0006965 | 0.0083396 | 0.0913214 |
| ts | wk.7200 | 2018-04-18 | 7200 | 0.0020413 | 0.0020389 | 0.0564488 | 0.2375895 |
| ts | wk.7200 | 2018-04-19 | 7200 | 0.0012612 | 0.0012603 | 0.0218598 | 0.1478506 |
| ts | wk.7200 | 2018-04-20 | 7200 | 0.0020460 | 0.0020435 | 0.0575700 | 0.2399375 |
| ts | wk.7200 | 2018-04-21 | 5 | 0.0025515 | 0.0025482 | 0.0750482 | 0.2739493 |
| ts | wk.7200 | 2018-04-23 | 7195 | 0.0045405 | 0.0045250 | 0.3622271 | 0.6018530 |
| ts | wk.7200 | 2018-04-24 | 7200 | 0.0011911 | 0.0011898 | 0.0309173 | 0.1758332 |
| ts | wk.7200 | 2018-04-25 | 7200 | 0.0061491 | 0.0061770 | 0.6819061 | 0.8257760 |
| ts | wk.7200 | 2018-04-26 | 7200 | 0.0120615 | 0.0121558 | 2.3133651 | 1.5209750 |
| ts | wk.7200 | 2018-04-27 | 7200 | 0.0008809 | 0.0008815 | 0.0183121 | 0.1353224 |
| ts | wk.7200 | 2018-04-28 | 5 | 0.0022232 | 0.0022257 | 0.0590493 | 0.2430007 |
| ts | wk.7200 | 2018-04-30 | 7195 | 0.0014982 | 0.0014966 | 0.0373042 | 0.1931430 |
| ts | wk.7200 | 2018-05-01 | 7200 | 0.0019000 | 0.0018972 | 0.0692565 | 0.2631662 |
| ts | wk.7200 | 2018-05-02 | 7200 | 0.0006549 | 0.0006552 | 0.0081629 | 0.0903490 |
| ts | wk.7200 | 2018-05-03 | 7200 | 0.0032227 | 0.0032306 | 0.1898766 | 0.4357484 |
| ts | wk.7200 | 2018-05-04 | 7200 | 0.0010356 | 0.0010365 | 0.0206772 | 0.1437958 |
| ts | wk.7200 | 2018-05-05 | 5 | 0.0010683 | 0.0010689 | 0.0136074 | 0.1166509 |
| ts | wk.7200 | 2018-05-07 | 7195 | 0.0010926 | 0.0010920 | 0.0213329 | 0.1460578 |
| ts | wk.7200 | 2018-05-08 | 7200 | 0.0008267 | 0.0008270 | 0.0120253 | 0.1096601 |
| ts | wk.7200 | 2018-05-09 | 7200 | 0.0041083 | 0.0040983 | 0.2381978 | 0.4880552 |
| ts | wk.7200 | 2018-05-10 | 7200 | 0.0013582 | 0.0013594 | 0.0377417 | 0.1942722 |
| ts | wk.7200 | 2018-05-11 | 7200 | 0.0007075 | 0.0007077 | 0.0085535 | 0.0924849 |
| ts | wk.7200 | 2018-05-12 | 5 | 0.0001095 | 0.0001095 | 0.0001436 | 0.0119818 |
| ts | wk.7200 | 2018-05-14 | 7195 | 0.0011009 | 0.0011002 | 0.0199433 | 0.1412207 |
| ts | wk.7200 | 2018-05-15 | 7200 | 0.0030283 | 0.0030211 | 0.1736171 | 0.4166739 |
| ts | wk.7200 | 2018-05-16 | 7200 | 0.0010725 | 0.0010733 | 0.0197746 | 0.1406220 |
| ts | wk.7200 | 2018-05-17 | 7200 | 0.0020266 | 0.0020244 | 0.0649055 | 0.2547655 |
| ts | wk.7200 | 2018-05-18 | 7200 | 0.0011067 | 0.0011061 | 0.0198144 | 0.1407637 |
| ts | wk.7200 | 2018-05-19 | 5 | 0.0001142 | 0.0001142 | 0.0001601 | 0.0126529 |
| ts | wk.7200 | 2018-05-21 | 7195 | 0.0034659 | 0.0034590 | 0.1709129 | 0.4134162 |
| ts | wk.7200 | 2018-05-22 | 7200 | 0.0008754 | 0.0008758 | 0.0118086 | 0.1086674 |
| ts | wk.7200 | 2018-05-23 | 7200 | 0.0057100 | 0.0057318 | 0.5327100 | 0.7298699 |
| ts | wk.7200 | 2018-05-24 | 7200 | 0.0049610 | 0.0049758 | 0.3572528 | 0.5977063 |
| ts | wk.7200 | 2018-05-25 | 7200 | 0.0016314 | 0.0016297 | 0.0431855 | 0.2078111 |
| ts | wk.7200 | 2018-05-26 | 5 | 0.0012219 | 0.0012212 | 0.0178230 | 0.1335027 |
| ts | wk.7200 | 2018-05-28 | 7195 | 0.0008202 | 0.0008195 | 0.0181591 | 0.1347557 |
| ts | wk.7200 | 2018-05-29 | 7200 | 0.0046705 | 0.0046847 | 0.3398942 | 0.5830045 |
| ts | wk.7200 | 2018-05-30 | 7200 | 0.0013343 | 0.0013346 | 0.0274149 | 0.1655743 |
| ts | wk.7200 | 2018-05-31 | 7200 | 0.0015399 | 0.0015416 | 0.0400234 | 0.2000584 |
| ts | wk.7200 | 2018-06-01 | 7200 | 0.0039110 | 0.0039006 | 0.2457693 | 0.4957513 |
| ts | wk.7200 | 2018-06-02 | 5 | 0.0064302 | 0.0064096 | 0.4896196 | 0.6997282 |
| ts | wk.7200 | 2018-06-04 | 7195 | 0.0009617 | 0.0009610 | 0.0173077 | 0.1315586 |
| ts | wk.7200 | 2018-06-05 | 7200 | 0.0006840 | 0.0006841 | 0.0090982 | 0.0953846 |
| ts | wk.7200 | 2018-06-06 | 7200 | 0.0020183 | 0.0020155 | 0.0663835 | 0.2576500 |
| ts | wk.7200 | 2018-06-07 | 7200 | 0.0020827 | 0.0020857 | 0.0739825 | 0.2719973 |
| ts | wk.7200 | 2018-06-08 | 7200 | 0.0016502 | 0.0016521 | 0.0493522 | 0.2221536 |
| ts | wk.7200 | 2018-06-09 | 5 | 0.0015453 | 0.0015465 | 0.0287397 | 0.1695279 |
| ts | wk.7200 | 2018-06-11 | 7195 | 0.0030990 | 0.0030933 | 0.1417896 | 0.3765496 |
| ts | wk.7200 | 2018-06-12 | 7200 | 0.0022481 | 0.0022453 | 0.0701022 | 0.2647683 |
| ts | wk.7200 | 2018-06-13 | 7200 | 0.0013500 | 0.0013487 | 0.0326133 | 0.1805914 |
| ts | wk.7200 | 2018-06-14 | 7200 | 0.0016997 | 0.0017008 | 0.0502138 | 0.2240844 |
| ts | wk.7200 | 2018-06-15 | 7200 | 0.0007272 | 0.0007272 | 0.0098713 | 0.0993543 |
| ts | wk.7200 | 2018-06-16 | 5 | 0.0002951 | 0.0002950 | 0.0010657 | 0.0326453 |
| ts | wk.7200 | 2018-06-18 | 7195 | 0.0014171 | 0.0014183 | 0.0292714 | 0.1710890 |
| ts | wk.7200 | 2018-06-19 | 7200 | 0.0052957 | 0.0053122 | 0.4010971 | 0.6333223 |
| ts | wk.7200 | 2018-06-20 | 7200 | 0.0009220 | 0.0009213 | 0.0190960 | 0.1381881 |
| ts | wk.7200 | 2018-06-21 | 7200 | 0.0019756 | 0.0019765 | 0.0688409 | 0.2623755 |
| ts | wk.7200 | 2018-06-22 | 7200 | 0.0006667 | 0.0006665 | 0.0087705 | 0.0936507 |
| ts | wk.7200 | 2018-06-23 | 5 | 0.0000121 | 0.0000121 | 0.0000018 | 0.0013275 |
| ts | wk.7200 | 2018-06-25 | 7195 | 0.0035498 | 0.0035570 | 0.1753596 | 0.4187596 |
| ts | wk.7200 | 2018-06-26 | 7200 | 0.0016588 | 0.0016587 | 0.0462353 | 0.2150239 |
| ts | wk.7200 | 2018-06-27 | 7200 | 0.0016475 | 0.0016468 | 0.0434671 | 0.2084877 |
| ts | wk.7200 | 2018-06-28 | 7200 | 0.0008682 | 0.0008679 | 0.0167661 | 0.1294839 |
| ts | wk.7200 | 2018-06-29 | 7200 | 0.0015295 | 0.0015279 | 0.0395188 | 0.1987934 |
| ts | wk.7200 | 2018-06-30 | 5 | 0.0017294 | 0.0017280 | 0.0365186 | 0.1910984 |
| ts | wk.7200 | 2018-07-02 | 7195 | 0.0010502 | 0.0010493 | 0.0212118 | 0.1456428 |
| ts | wk.7200 | 2018-07-03 | 7200 | 0.0012720 | 0.0012733 | 0.0349115 | 0.1868462 |
| ts | wk.7200 | 2018-07-04 | 7200 | 0.0010274 | 0.0010281 | 0.0163644 | 0.1279235 |
| ts | wk.7200 | 2018-07-05 | 7200 | 0.0009804 | 0.0009800 | 0.0141518 | 0.1189613 |
| ts | wk.7200 | 2018-07-06 | 7200 | 0.0008002 | 0.0008006 | 0.0130965 | 0.1144399 |
| ts | wk.7200 | 2018-07-07 | 5 | 0.0016406 | 0.0016419 | 0.0329496 | 0.1815203 |
| ts | yr.1440 | 2018-01-03 | 1439 | 0.0007286 | 0.0007281 | 0.0115161 | 0.1073129 |
| ts | yr.1440 | 2018-01-04 | 1440 | 0.0022569 | 0.0022540 | 0.0734649 | 0.2710440 |
| ts | yr.1440 | 2018-01-05 | 1440 | 0.0032410 | 0.0032344 | 0.1681745 | 0.4100909 |
| ts | yr.1440 | 2018-01-06 | 1 | 0.0028941 | 0.0028899 | 0.1064477 | 0.3262632 |
| ts | yr.1440 | 2018-01-08 | 1439 | 0.0008377 | 0.0008373 | 0.0126258 | 0.1123644 |
| ts | yr.1440 | 2018-01-09 | 1440 | 0.0034149 | 0.0034220 | 0.1811900 | 0.4256642 |
| ts | yr.1440 | 2018-01-10 | 1440 | 0.0069793 | 0.0070122 | 0.8300368 | 0.9110636 |
| ts | yr.1440 | 2018-01-11 | 1440 | 0.0020285 | 0.0020267 | 0.0695032 | 0.2636345 |
| ts | yr.1440 | 2018-01-12 | 1440 | 0.0009401 | 0.0009403 | 0.0187880 | 0.1370693 |
| ts | yr.1440 | 2018-01-13 | 1 | 0.0021296 | 0.0021319 | 0.0561425 | 0.2369441 |
| ts | yr.1440 | 2018-01-15 | 1439 | 0.0031574 | 0.0031632 | 0.1429524 | 0.3780904 |
| ts | yr.1440 | 2018-01-16 | 1440 | 0.0020256 | 0.0020232 | 0.0640146 | 0.2530111 |
| ts | yr.1440 | 2018-01-17 | 1440 | 0.0025736 | 0.0025692 | 0.1147251 | 0.3387109 |
| ts | yr.1440 | 2018-01-18 | 1440 | 0.0011139 | 0.0011150 | 0.0300460 | 0.1733379 |
| ts | yr.1440 | 2018-01-19 | 1440 | 0.0031785 | 0.0031845 | 0.1461572 | 0.3823051 |
| ts | yr.1440 | 2018-01-20 | 1 | 0.0025213 | 0.0025245 | 0.0784868 | 0.2801549 |
| ts | yr.1440 | 2018-01-22 | 1439 | 0.0011068 | 0.0011060 | 0.0292804 | 0.1711151 |
| ts | yr.1440 | 2018-01-23 | 1440 | 0.0024627 | 0.0024671 | 0.1107709 | 0.3328226 |
| ts | yr.1440 | 2018-01-24 | 1440 | 0.0057013 | 0.0057232 | 0.5301945 | 0.7281446 |
| ts | yr.1440 | 2018-01-25 | 1440 | 0.0018044 | 0.0018061 | 0.0604222 | 0.2458092 |
| ts | yr.1440 | 2018-01-26 | 1440 | 0.0029688 | 0.0029750 | 0.1745773 | 0.4178245 |
| ts | yr.1440 | 2018-01-27 | 1 | 0.0071595 | 0.0071853 | 0.6136259 | 0.7833428 |
| ts | yr.1440 | 2018-01-29 | 1439 | 0.0026351 | 0.0026299 | 0.1238625 | 0.3519410 |
| ts | yr.1440 | 2018-01-30 | 1440 | 0.0014949 | 0.0014964 | 0.0367623 | 0.1917349 |
| ts | yr.1440 | 2018-01-31 | 1440 | 0.0020716 | 0.0020674 | 0.1014602 | 0.3185282 |
| ts | yr.1440 | 2018-02-01 | 1440 | 0.0027117 | 0.0027065 | 0.1241716 | 0.3523799 |
| ts | yr.1440 | 2018-02-02 | 1440 | 0.0045717 | 0.0045563 | 0.3732799 | 0.6109664 |
| ts | yr.1440 | 2018-02-03 | 1 | 0.0070643 | 0.0070394 | 0.5972853 | 0.7728423 |
| ts | yr.1440 | 2018-02-05 | 1439 | 0.0027286 | 0.0027340 | 0.1329068 | 0.3645639 |
| ts | yr.1440 | 2018-02-06 | 1440 | 0.0019107 | 0.0019117 | 0.0742761 | 0.2725365 |
| ts | yr.1440 | 2018-02-07 | 1440 | 0.0021799 | 0.0021832 | 0.0797766 | 0.2824475 |
| ts | yr.1440 | 2018-02-08 | 1440 | 0.0027627 | 0.0027637 | 0.1335827 | 0.3654897 |
| ts | yr.1440 | 2018-02-09 | 1440 | 0.0020273 | 0.0020275 | 0.0733162 | 0.2707697 |
| ts | yr.1440 | 2018-02-10 | 1 | 0.0004384 | 0.0004383 | 0.0022725 | 0.0476703 |
| ts | yr.1440 | 2018-02-12 | 1439 | 0.0015453 | 0.0015469 | 0.0396262 | 0.1990634 |
| ts | yr.1440 | 2018-02-13 | 1440 | 0.0066779 | 0.0067093 | 0.7417352 | 0.8612405 |
| ts | yr.1440 | 2018-02-14 | 1440 | 0.0047591 | 0.0047739 | 0.3441722 | 0.5866619 |
| ts | yr.1440 | 2018-02-15 | 1440 | 0.0045304 | 0.0045426 | 0.2775753 | 0.5268541 |
| ts | yr.1440 | 2018-02-16 | 1440 | 0.0011766 | 0.0011771 | 0.0263064 | 0.1621925 |
| ts | yr.1440 | 2018-02-17 | 1 | 0.0015973 | 0.0015960 | 0.0287414 | 0.1695328 |
| ts | yr.1440 | 2018-02-19 | 1439 | 0.0023227 | 0.0023194 | 0.0767605 | 0.2770569 |
| ts | yr.1440 | 2018-02-20 | 1440 | 0.0043175 | 0.0043060 | 0.2612627 | 0.5111386 |
| ts | yr.1440 | 2018-02-21 | 1440 | 0.0028600 | 0.0028545 | 0.1260728 | 0.3550673 |
| ts | yr.1440 | 2018-02-22 | 1440 | 0.0051380 | 0.0051556 | 0.4059544 | 0.6371455 |
| ts | yr.1440 | 2018-02-23 | 1440 | 0.0012329 | 0.0012318 | 0.0275998 | 0.1661320 |
| ts | yr.1440 | 2018-02-24 | 1 | 0.0013198 | 0.0013190 | 0.0198509 | 0.1408931 |
| ts | yr.1440 | 2018-02-26 | 1439 | 0.0017950 | 0.0017963 | 0.0479682 | 0.2190165 |
| ts | yr.1440 | 2018-02-27 | 1440 | 0.0020228 | 0.0020191 | 0.0865509 | 0.2941954 |
| ts | yr.1440 | 2018-02-28 | 1440 | 0.0024919 | 0.0024970 | 0.1178464 | 0.3432877 |
| ts | yr.1440 | 2018-03-01 | 1440 | 0.0016436 | 0.0016431 | 0.0462300 | 0.2150116 |
| ts | yr.1440 | 2018-03-02 | 1440 | 0.0048190 | 0.0048344 | 0.3471929 | 0.5892308 |
| ts | yr.1440 | 2018-03-03 | 1 | 0.0047346 | 0.0047458 | 0.2529617 | 0.5029530 |
| ts | yr.1440 | 2018-03-05 | 1439 | 0.0018016 | 0.0018001 | 0.0612390 | 0.2474651 |
| ts | yr.1440 | 2018-03-06 | 1440 | 0.0011791 | 0.0011788 | 0.0240258 | 0.1550026 |
| ts | yr.1440 | 2018-03-07 | 1440 | 0.0029573 | 0.0029629 | 0.1258242 | 0.3547171 |
| ts | yr.1440 | 2018-03-08 | 1440 | 0.0011230 | 0.0011222 | 0.0184723 | 0.1359129 |
| ts | yr.1440 | 2018-03-09 | 1440 | 0.0055152 | 0.0054987 | 0.3725929 | 0.6104039 |
| ts | yr.1440 | 2018-03-10 | 1 | 0.0056884 | 0.0056723 | 0.3651129 | 0.6042457 |
| ts | yr.1440 | 2018-03-12 | 1439 | 0.0020961 | 0.0020989 | 0.0657168 | 0.2563528 |
| ts | yr.1440 | 2018-03-13 | 1440 | 0.0033617 | 0.0033527 | 0.2064085 | 0.4543220 |
| ts | yr.1440 | 2018-03-14 | 1440 | 0.0013898 | 0.0013914 | 0.0367829 | 0.1917888 |
| ts | yr.1440 | 2018-03-15 | 1440 | 0.0023566 | 0.0023602 | 0.0817396 | 0.2859014 |
| ts | yr.1440 | 2018-03-16 | 1440 | 0.0029440 | 0.0029500 | 0.1359519 | 0.3687166 |
| ts | yr.1440 | 2018-03-17 | 1 | 0.0033886 | 0.0033944 | 0.1298567 | 0.3603564 |
| ts | yr.1440 | 2018-03-19 | 1439 | 0.0009625 | 0.0009622 | 0.0159425 | 0.1262636 |
| ts | yr.1440 | 2018-03-20 | 1440 | 0.0027069 | 0.0027025 | 0.1002939 | 0.3166921 |
| ts | yr.1440 | 2018-03-21 | 1440 | 0.0015849 | 0.0015871 | 0.0513978 | 0.2267107 |
| ts | yr.1440 | 2018-03-22 | 1440 | 0.0032062 | 0.0032131 | 0.1546442 | 0.3932483 |
| ts | yr.1440 | 2018-03-23 | 1440 | 0.0029472 | 0.0029523 | 0.1132850 | 0.3365784 |
| ts | yr.1440 | 2018-03-24 | 1 | 0.0051780 | 0.0051914 | 0.2971834 | 0.5451453 |
| ts | yr.1440 | 2018-03-26 | 1439 | 0.0032517 | 0.0032454 | 0.1379356 | 0.3713968 |
| ts | yr.1440 | 2018-03-27 | 1440 | 0.0024060 | 0.0024025 | 0.0771220 | 0.2777085 |
| ts | yr.1440 | 2018-03-28 | 1440 | 0.0052441 | 0.0052204 | 0.5298671 | 0.7279197 |
| ts | yr.1440 | 2018-03-29 | 1440 | 0.0026057 | 0.0026103 | 0.1091210 | 0.3303346 |
| ts | yr.1440 | 2018-03-30 | 1440 | 0.0016504 | 0.0016520 | 0.0375683 | 0.1938253 |
| ts | yr.1440 | 2018-03-31 | 1 | 0.0013316 | 0.0013325 | 0.0200835 | 0.1417161 |
| ts | yr.1440 | 2018-04-02 | 1439 | 0.0015272 | 0.0015288 | 0.0507477 | 0.2252724 |
| ts | yr.1440 | 2018-04-03 | 1440 | 0.0027708 | 0.0027647 | 0.1400728 | 0.3742630 |
| ts | yr.1440 | 2018-04-04 | 1440 | 0.0015243 | 0.0015265 | 0.0540027 | 0.2323847 |
| ts | yr.1440 | 2018-04-05 | 1440 | 0.0034801 | 0.0034721 | 0.1825493 | 0.4272579 |
| ts | yr.1440 | 2018-04-06 | 1440 | 0.0017790 | 0.0017816 | 0.0632165 | 0.2514290 |
| ts | yr.1440 | 2018-04-07 | 1 | 0.0041705 | 0.0041792 | 0.2005684 | 0.4478487 |
| ts | yr.1440 | 2018-04-09 | 1439 | 0.0012204 | 0.0012198 | 0.0242368 | 0.1556818 |
| ts | yr.1440 | 2018-04-10 | 1440 | 0.0027450 | 0.0027402 | 0.1094158 | 0.3307806 |
| ts | yr.1440 | 2018-04-11 | 1440 | 0.0020957 | 0.0020988 | 0.0716817 | 0.2677344 |
| ts | yr.1440 | 2018-04-12 | 1440 | 0.0023470 | 0.0023426 | 0.0993388 | 0.3151806 |
| ts | yr.1440 | 2018-04-13 | 1440 | 0.0014241 | 0.0014224 | 0.0394478 | 0.1986148 |
| ts | yr.1440 | 2018-04-14 | 1 | 0.0002794 | 0.0002794 | 0.0008994 | 0.0299893 |
| ts | yr.1440 | 2018-04-16 | 1439 | 0.0017028 | 0.0017041 | 0.0377932 | 0.1944047 |
| ts | yr.1440 | 2018-04-17 | 1440 | 0.0008719 | 0.0008725 | 0.0125108 | 0.1118516 |
| ts | yr.1440 | 2018-04-18 | 1440 | 0.0018023 | 0.0018003 | 0.0459748 | 0.2144173 |
| ts | yr.1440 | 2018-04-19 | 1440 | 0.0008828 | 0.0008822 | 0.0120747 | 0.1098849 |
| ts | yr.1440 | 2018-04-20 | 1440 | 0.0015771 | 0.0015756 | 0.0351354 | 0.1874444 |
| ts | yr.1440 | 2018-04-21 | 1 | 0.0025328 | 0.0025296 | 0.0739536 | 0.2719442 |
| ts | yr.1440 | 2018-04-23 | 1439 | 0.0040095 | 0.0039958 | 0.3188367 | 0.5646563 |
| ts | yr.1440 | 2018-04-24 | 1440 | 0.0008568 | 0.0008561 | 0.0186719 | 0.1366451 |
| ts | yr.1440 | 2018-04-25 | 1440 | 0.0023206 | 0.0023165 | 0.0971058 | 0.3116181 |
| ts | yr.1440 | 2018-04-26 | 1440 | 0.0012891 | 0.0012903 | 0.0292572 | 0.1710473 |
| ts | yr.1440 | 2018-04-27 | 1440 | 0.0009652 | 0.0009660 | 0.0195378 | 0.1397777 |
| ts | yr.1440 | 2018-04-28 | 1 | 0.0021960 | 0.0021984 | 0.0576079 | 0.2400164 |
| ts | yr.1440 | 2018-04-30 | 1439 | 0.0013754 | 0.0013741 | 0.0318968 | 0.1785967 |
| ts | yr.1440 | 2018-05-01 | 1440 | 0.0018091 | 0.0018065 | 0.0636554 | 0.2523003 |
| ts | yr.1440 | 2018-05-02 | 1440 | 0.0006240 | 0.0006242 | 0.0068311 | 0.0826506 |
| ts | yr.1440 | 2018-05-03 | 1440 | 0.0031199 | 0.0031277 | 0.1863365 | 0.4316671 |
| ts | yr.1440 | 2018-05-04 | 1440 | 0.0008645 | 0.0008651 | 0.0159982 | 0.1264838 |
| ts | yr.1440 | 2018-05-05 | 1 | 0.0011169 | 0.0011175 | 0.0148753 | 0.1219645 |
| ts | yr.1440 | 2018-05-07 | 1439 | 0.0011128 | 0.0011121 | 0.0220492 | 0.1484896 |
| ts | yr.1440 | 2018-05-08 | 1440 | 0.0007871 | 0.0007874 | 0.0115642 | 0.1075371 |
| ts | yr.1440 | 2018-05-09 | 1440 | 0.0042863 | 0.0042756 | 0.2557127 | 0.5056804 |
| ts | yr.1440 | 2018-05-10 | 1440 | 0.0014158 | 0.0014172 | 0.0399857 | 0.1999642 |
| ts | yr.1440 | 2018-05-11 | 1440 | 0.0008593 | 0.0008596 | 0.0126576 | 0.1125061 |
| ts | yr.1440 | 2018-05-12 | 1 | 0.0000814 | 0.0000814 | 0.0000793 | 0.0089056 |
| ts | yr.1440 | 2018-05-14 | 1439 | 0.0009817 | 0.0009810 | 0.0184651 | 0.1358862 |
| ts | yr.1440 | 2018-05-15 | 1440 | 0.0030468 | 0.0030394 | 0.1779800 | 0.4218768 |
| ts | yr.1440 | 2018-05-16 | 1440 | 0.0011532 | 0.0011541 | 0.0236384 | 0.1537478 |
| ts | yr.1440 | 2018-05-17 | 1440 | 0.0020097 | 0.0020072 | 0.0693756 | 0.2633925 |
| ts | yr.1440 | 2018-05-18 | 1440 | 0.0011827 | 0.0011818 | 0.0239644 | 0.1548044 |
| ts | yr.1440 | 2018-05-19 | 1 | 0.0001350 | 0.0001350 | 0.0002237 | 0.0149578 |
| ts | yr.1440 | 2018-05-21 | 1439 | 0.0036315 | 0.0036242 | 0.1807371 | 0.4251319 |
| ts | yr.1440 | 2018-05-22 | 1440 | 0.0010908 | 0.0010916 | 0.0189772 | 0.1377577 |
| ts | yr.1440 | 2018-05-23 | 1440 | 0.0057808 | 0.0058035 | 0.5560307 | 0.7456747 |
| ts | yr.1440 | 2018-05-24 | 1440 | 0.0045584 | 0.0045714 | 0.3154355 | 0.5616364 |
| ts | yr.1440 | 2018-05-25 | 1440 | 0.0019992 | 0.0019966 | 0.0644089 | 0.2537892 |
| ts | yr.1440 | 2018-05-26 | 1 | 0.0012669 | 0.0012661 | 0.0191556 | 0.1384039 |
| ts | yr.1440 | 2018-05-28 | 1439 | 0.0008982 | 0.0008974 | 0.0204749 | 0.1430905 |
| ts | yr.1440 | 2018-05-29 | 1440 | 0.0046156 | 0.0046295 | 0.3307554 | 0.5751134 |
| ts | yr.1440 | 2018-05-30 | 1440 | 0.0014692 | 0.0014692 | 0.0340658 | 0.1845691 |
| ts | yr.1440 | 2018-05-31 | 1440 | 0.0013646 | 0.0013659 | 0.0304835 | 0.1745952 |
| ts | yr.1440 | 2018-06-01 | 1440 | 0.0044958 | 0.0044827 | 0.3110066 | 0.5576797 |
| ts | yr.1440 | 2018-06-02 | 1 | 0.0064868 | 0.0064658 | 0.4982169 | 0.7058448 |
| ts | yr.1440 | 2018-06-04 | 1439 | 0.0012125 | 0.0012115 | 0.0245189 | 0.1565852 |
| ts | yr.1440 | 2018-06-05 | 1440 | 0.0008150 | 0.0008149 | 0.0115294 | 0.1073752 |
| ts | yr.1440 | 2018-06-06 | 1440 | 0.0024150 | 0.0024113 | 0.0902119 | 0.3003529 |
| ts | yr.1440 | 2018-06-07 | 1440 | 0.0018571 | 0.0018596 | 0.0608236 | 0.2466245 |
| ts | yr.1440 | 2018-06-08 | 1440 | 0.0015612 | 0.0015629 | 0.0435067 | 0.2085825 |
| ts | yr.1440 | 2018-06-09 | 1 | 0.0015622 | 0.0015635 | 0.0293723 | 0.1713835 |
| ts | yr.1440 | 2018-06-11 | 1439 | 0.0033370 | 0.0033300 | 0.1714798 | 0.4141011 |
| ts | yr.1440 | 2018-06-12 | 1440 | 0.0022838 | 0.0022808 | 0.0728401 | 0.2698891 |
| ts | yr.1440 | 2018-06-13 | 1440 | 0.0013310 | 0.0013297 | 0.0305683 | 0.1748379 |
| ts | yr.1440 | 2018-06-14 | 1440 | 0.0020519 | 0.0020538 | 0.0686272 | 0.2619679 |
| ts | yr.1440 | 2018-06-15 | 1440 | 0.0006625 | 0.0006623 | 0.0086253 | 0.0928725 |
| ts | yr.1440 | 2018-06-16 | 1 | 0.0002994 | 0.0002993 | 0.0010969 | 0.0331195 |
| ts | yr.1440 | 2018-06-18 | 1439 | 0.0013561 | 0.0013572 | 0.0283490 | 0.1683716 |
| ts | yr.1440 | 2018-06-19 | 1440 | 0.0050897 | 0.0051049 | 0.3703398 | 0.6085555 |
| ts | yr.1440 | 2018-06-20 | 1440 | 0.0016890 | 0.0016873 | 0.0424919 | 0.2061357 |
| ts | yr.1440 | 2018-06-21 | 1440 | 0.0023272 | 0.0023267 | 0.0843180 | 0.2903756 |
| ts | yr.1440 | 2018-06-22 | 1440 | 0.0009191 | 0.0009184 | 0.0178552 | 0.1336232 |
| ts | yr.1440 | 2018-06-23 | 1 | 0.0000145 | 0.0000145 | 0.0000026 | 0.0015975 |
| ts | yr.1440 | 2018-06-25 | 1439 | 0.0031427 | 0.0031486 | 0.1407032 | 0.3751043 |
| ts | yr.1440 | 2018-06-26 | 1440 | 0.0014587 | 0.0014573 | 0.0470950 | 0.2170139 |
| ts | yr.1440 | 2018-06-27 | 1440 | 0.0016095 | 0.0016074 | 0.0564145 | 0.2375173 |
| ts | yr.1440 | 2018-06-28 | 1440 | 0.0011744 | 0.0011734 | 0.0258519 | 0.1607852 |
| ts | yr.1440 | 2018-06-29 | 1440 | 0.0022784 | 0.0022752 | 0.0781593 | 0.2795699 |
| ts | yr.1440 | 2018-06-30 | 1 | 0.0017049 | 0.0017034 | 0.0354899 | 0.1883877 |
| ts | yr.1440 | 2018-07-02 | 1439 | 0.0015521 | 0.0015504 | 0.0413679 | 0.2033911 |
| ts | yr.1440 | 2018-07-03 | 1440 | 0.0014004 | 0.0014012 | 0.0369248 | 0.1921582 |
| ts | yr.1440 | 2018-07-04 | 1440 | 0.0007003 | 0.0007006 | 0.0087622 | 0.0936068 |
| ts | yr.1440 | 2018-07-05 | 1440 | 0.0010737 | 0.0010730 | 0.0188191 | 0.1371828 |
| ts | yr.1440 | 2018-07-06 | 1440 | 0.0009016 | 0.0009019 | 0.0152644 | 0.1235490 |
| ts | yr.1440 | 2018-07-07 | 1 | 0.0016391 | 0.0016405 | 0.0328911 | 0.1813590 |
plt_s2 %>%
kbl('html', caption = 'Data Sample', escape = FALSE) %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')| Model | Period | index | N | open.mape | open.smape | open.mse | open.rmse |
|---|---|---|---|---|---|---|---|
| tbats | dy.qt | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.qt | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.qt | 2018-01-05 | 1440 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| tbats | dy.qt | 2018-01-06 | 1 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| tbats | dy.qt | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050751 | 0.4528522 |
| tbats | dy.qt | 2018-01-09 | 1440 | 0.0012943 | 0.0012931 | 0.0419181 | 0.2047390 |
| tbats | dy.qt | 2018-01-10 | 1440 | 0.0073048 | 0.0073400 | 0.8879488 | 0.9423103 |
| tbats | dy.qt | 2018-01-11 | 1440 | 0.0103775 | 0.0104334 | 1.4110712 | 1.1878852 |
| tbats | dy.qt | 2018-01-12 | 1440 | 0.0130046 | 0.0130904 | 2.1649021 | 1.4713606 |
| tbats | dy.qt | 2018-01-13 | 1 | 0.0147054 | 0.0148143 | 2.7456490 | 1.6570000 |
| tbats | dy.qt | 2018-01-15 | 1439 | 0.0177735 | 0.0179342 | 4.0444477 | 2.0110812 |
| tbats | dy.qt | 2018-01-16 | 1440 | 0.0175204 | 0.0176763 | 3.9235329 | 1.9807910 |
| tbats | dy.qt | 2018-01-17 | 1440 | 0.0173391 | 0.0174925 | 3.8604893 | 1.9648128 |
| tbats | dy.qt | 2018-01-18 | 1440 | 0.0132828 | 0.0133725 | 2.2636575 | 1.5045456 |
| tbats | dy.qt | 2018-01-19 | 1440 | 0.0169647 | 0.0171110 | 3.6821392 | 1.9188901 |
| tbats | dy.qt | 2018-01-20 | 1 | 0.0163738 | 0.0165090 | 3.4040250 | 1.8450000 |
| tbats | dy.qt | 2018-01-22 | 1439 | 0.0164475 | 0.0165846 | 3.4523110 | 1.8580396 |
| tbats | dy.qt | 2018-01-23 | 1440 | 0.0180156 | 0.0181820 | 4.1856644 | 2.0458896 |
| tbats | dy.qt | 2018-01-24 | 1440 | 0.0268881 | 0.0272614 | 9.3470521 | 3.0572949 |
| tbats | dy.qt | 2018-01-25 | 1440 | 0.0322722 | 0.0328036 | 13.2754630 | 3.6435509 |
| tbats | dy.qt | 2018-01-26 | 1440 | 0.0318377 | 0.0323591 | 13.0263583 | 3.6092047 |
| tbats | dy.qt | 2018-01-27 | 1 | 0.0359514 | 0.0366094 | 16.4106010 | 4.0510000 |
| tbats | dy.qt | 2018-01-29 | 1439 | 0.0339983 | 0.0345871 | 14.6966838 | 3.8336254 |
| tbats | dy.qt | 2018-01-30 | 1440 | 0.0346458 | 0.0352574 | 15.2604667 | 3.9064647 |
| tbats | dy.qt | 2018-01-31 | 1440 | 0.0333584 | 0.0339260 | 14.1707246 | 3.7644023 |
| tbats | dy.qt | 2018-02-01 | 1440 | 0.0288410 | 0.0292640 | 10.5843271 | 3.2533563 |
| tbats | dy.qt | 2018-02-02 | 1440 | 0.0249175 | 0.0252362 | 7.9895620 | 2.8265813 |
| tbats | dy.qt | 2018-02-03 | 1 | 0.0222400 | 0.0224901 | 6.2800360 | 2.5060000 |
| tbats | dy.qt | 2018-02-05 | 1439 | 0.0247250 | 0.0250364 | 7.8101566 | 2.7946657 |
| tbats | dy.qt | 2018-02-06 | 1440 | 0.0316136 | 0.0321241 | 12.7564999 | 3.5716243 |
| tbats | dy.qt | 2018-02-07 | 1440 | 0.0298147 | 0.0302673 | 11.3204578 | 3.3645888 |
| tbats | dy.qt | 2018-02-08 | 1440 | 0.0295570 | 0.0300045 | 11.1915858 | 3.3453828 |
| tbats | dy.qt | 2018-02-09 | 1440 | 0.0340752 | 0.0346683 | 14.8008132 | 3.8471825 |
| tbats | dy.qt | 2018-02-10 | 1 | 0.0344693 | 0.0350738 | 15.0854560 | 3.8840000 |
| tbats | dy.qt | 2018-02-12 | 1439 | 0.0355512 | 0.0361948 | 16.0525253 | 4.0065603 |
| tbats | dy.qt | 2018-02-13 | 1440 | 0.0415012 | 0.0423895 | 22.0797777 | 4.6989124 |
| tbats | dy.qt | 2018-02-14 | 1440 | 0.0478455 | 0.0490216 | 29.1477209 | 5.3988629 |
| tbats | dy.qt | 2018-02-15 | 1440 | 0.0548283 | 0.0563755 | 38.2107906 | 6.1814877 |
| tbats | dy.qt | 2018-02-16 | 1440 | 0.0585071 | 0.0602717 | 43.4960112 | 6.5951506 |
| tbats | dy.qt | 2018-02-17 | 1 | 0.0565673 | 0.0582138 | 40.6278760 | 6.3740000 |
| tbats | dy.qt | 2018-02-19 | 1439 | 0.0018810 | 0.0018789 | 0.0502889 | 0.2242519 |
| tbats | dy.qt | 2018-02-20 | 1440 | 0.0039150 | 0.0039051 | 0.2257944 | 0.4751782 |
| tbats | dy.qt | 2018-02-21 | 1440 | 0.0025510 | 0.0025468 | 0.0960670 | 0.3099467 |
| tbats | dy.qt | 2018-02-22 | 1440 | 0.0053739 | 0.0053927 | 0.4358929 | 0.6602219 |
| tbats | dy.qt | 2018-02-23 | 1440 | 0.0010663 | 0.0010658 | 0.0193807 | 0.1392147 |
| tbats | dy.qt | 2018-02-24 | 1 | 0.0012813 | 0.0012805 | 0.0187112 | 0.1367888 |
| tbats | dy.qt | 2018-02-26 | 1439 | 0.0017207 | 0.0017224 | 0.0487130 | 0.2207101 |
| tbats | dy.qt | 2018-02-27 | 1440 | 0.0017627 | 0.0017597 | 0.0692587 | 0.2631706 |
| tbats | dy.qt | 2018-02-28 | 1440 | 0.0028550 | 0.0028609 | 0.1383402 | 0.3719411 |
| tbats | dy.qt | 2018-03-01 | 1440 | 0.0014258 | 0.0014257 | 0.0407300 | 0.2018167 |
| tbats | dy.qt | 2018-03-02 | 1440 | 0.0044554 | 0.0044691 | 0.3069946 | 0.5540710 |
| tbats | dy.qt | 2018-03-03 | 1 | 0.0047471 | 0.0047584 | 0.2543040 | 0.5042856 |
| tbats | dy.qt | 2018-03-05 | 1439 | 0.0020813 | 0.0020805 | 0.0656674 | 0.2562565 |
| tbats | dy.qt | 2018-03-06 | 1440 | 0.0010507 | 0.0010510 | 0.0191561 | 0.1384056 |
| tbats | dy.qt | 2018-03-07 | 1440 | 0.0032845 | 0.0032912 | 0.1519726 | 0.3898366 |
| tbats | dy.qt | 2018-03-08 | 1440 | 0.0006005 | 0.0006004 | 0.0064385 | 0.0802403 |
| tbats | dy.qt | 2018-03-09 | 1440 | 0.0048093 | 0.0047965 | 0.2887926 | 0.5373943 |
| tbats | dy.qt | 2018-03-10 | 1 | 0.0057372 | 0.0057207 | 0.3713635 | 0.6093960 |
| tbats | dy.qt | 2018-03-12 | 1439 | 0.0023390 | 0.0023423 | 0.0759089 | 0.2755157 |
| tbats | dy.qt | 2018-03-13 | 1440 | 0.0028999 | 0.0028931 | 0.1572071 | 0.3964935 |
| tbats | dy.qt | 2018-03-14 | 1440 | 0.0013291 | 0.0013305 | 0.0331019 | 0.1819393 |
| tbats | dy.qt | 2018-03-15 | 1440 | 0.0023845 | 0.0023882 | 0.0828577 | 0.2878502 |
| tbats | dy.qt | 2018-03-16 | 1440 | 0.0033274 | 0.0033348 | 0.1665281 | 0.4080786 |
| tbats | dy.qt | 2018-03-17 | 1 | 0.0034003 | 0.0034061 | 0.1307541 | 0.3615994 |
| tbats | dy.qt | 2018-03-19 | 1439 | 0.0011850 | 0.0011852 | 0.0217987 | 0.1476438 |
| tbats | dy.qt | 2018-03-20 | 1440 | 0.0022856 | 0.0022823 | 0.0757474 | 0.2752225 |
| tbats | dy.qt | 2018-03-21 | 1440 | 0.0017213 | 0.0017237 | 0.0554248 | 0.2354247 |
| tbats | dy.qt | 2018-03-22 | 1440 | 0.0034462 | 0.0034537 | 0.1688976 | 0.4109715 |
| tbats | dy.qt | 2018-03-23 | 1440 | 0.0032304 | 0.0032366 | 0.1360697 | 0.3688763 |
| tbats | dy.qt | 2018-03-24 | 1 | 0.0051877 | 0.0052012 | 0.2983075 | 0.5461754 |
| tbats | dy.qt | 2018-03-26 | 1439 | 0.0028861 | 0.0028807 | 0.1198734 | 0.3462273 |
| tbats | dy.qt | 2018-03-27 | 1440 | 0.0019733 | 0.0019708 | 0.0548570 | 0.2342156 |
| tbats | dy.qt | 2018-03-28 | 1440 | 0.0054888 | 0.0054627 | 0.5830772 | 0.7635949 |
| tbats | dy.qt | 2018-03-29 | 1440 | 0.0026981 | 0.0027027 | 0.1069173 | 0.3269821 |
| tbats | dy.qt | 2018-03-30 | 1440 | 0.0017376 | 0.0017394 | 0.0399285 | 0.1998213 |
| tbats | dy.qt | 2018-03-31 | 1 | 0.0013576 | 0.0013585 | 0.0208770 | 0.1444887 |
| tbats | dy.qt | 2018-04-02 | 1439 | 0.0011295 | 0.0011310 | 0.0377658 | 0.1943343 |
| tbats | dy.qt | 2018-04-03 | 1440 | 0.0027903 | 0.0027837 | 0.1511955 | 0.3888386 |
| tbats | dy.qt | 2018-04-04 | 1440 | 0.0017291 | 0.0017314 | 0.0600898 | 0.2451322 |
| tbats | dy.qt | 2018-04-05 | 1440 | 0.0028588 | 0.0028526 | 0.1439445 | 0.3794002 |
| tbats | dy.qt | 2018-04-06 | 1440 | 0.0017676 | 0.0017703 | 0.0636784 | 0.2523457 |
| tbats | dy.qt | 2018-04-07 | 1 | 0.0041444 | 0.0041530 | 0.1980616 | 0.4450411 |
| tbats | dy.qt | 2018-04-09 | 1439 | 0.0009020 | 0.0009017 | 0.0139755 | 0.1182182 |
| tbats | dy.qt | 2018-04-10 | 1440 | 0.0024381 | 0.0024343 | 0.0871189 | 0.2951591 |
| tbats | dy.qt | 2018-04-11 | 1440 | 0.0020890 | 0.0020920 | 0.0689188 | 0.2625239 |
| tbats | dy.qt | 2018-04-12 | 1440 | 0.0022921 | 0.0022879 | 0.0981073 | 0.3132209 |
| tbats | dy.qt | 2018-04-13 | 1440 | 0.0015270 | 0.0015252 | 0.0423808 | 0.2058660 |
| tbats | dy.qt | 2018-04-14 | 1 | 0.0003289 | 0.0003289 | 0.0012460 | 0.0352982 |
| tbats | dy.qt | 2018-04-16 | 1439 | 0.0012836 | 0.0012842 | 0.0236461 | 0.1537730 |
| tbats | dy.qt | 2018-04-17 | 1440 | 0.0006967 | 0.0006970 | 0.0083520 | 0.0913892 |
| tbats | dy.qt | 2018-04-18 | 1440 | 0.0020366 | 0.0020342 | 0.0562271 | 0.2371224 |
| tbats | dy.qt | 2018-04-19 | 1440 | 0.0012621 | 0.0012611 | 0.0218887 | 0.1479484 |
| tbats | dy.qt | 2018-04-20 | 1440 | 0.0020490 | 0.0020465 | 0.0577120 | 0.2402333 |
| tbats | dy.qt | 2018-04-21 | 1 | 0.0025545 | 0.0025513 | 0.0752254 | 0.2742725 |
| tbats | dy.qt | 2018-04-23 | 1439 | 0.0045611 | 0.0045455 | 0.3645420 | 0.6037731 |
| tbats | dy.qt | 2018-04-24 | 1440 | 0.0011920 | 0.0011908 | 0.0309522 | 0.1759325 |
| tbats | dy.qt | 2018-04-25 | 1440 | 0.0027018 | 0.0026968 | 0.1197275 | 0.3460166 |
| tbats | dy.qt | 2018-04-26 | 1440 | 0.0010282 | 0.0010289 | 0.0189114 | 0.1375186 |
| tbats | dy.qt | 2018-04-27 | 1440 | 0.0008721 | 0.0008727 | 0.0162402 | 0.1274369 |
| tbats | dy.qt | 2018-04-28 | 1 | 0.0022253 | 0.0022278 | 0.0591608 | 0.2432299 |
| tbats | dy.qt | 2018-04-30 | 1439 | 0.0014960 | 0.0014945 | 0.0372243 | 0.1929359 |
| tbats | dy.qt | 2018-05-01 | 1440 | 0.0019179 | 0.0019150 | 0.0704245 | 0.2653761 |
| tbats | dy.qt | 2018-05-02 | 1440 | 0.0006541 | 0.0006544 | 0.0081468 | 0.0902595 |
| tbats | dy.qt | 2018-05-03 | 1440 | 0.0032235 | 0.0032314 | 0.1899514 | 0.4358341 |
| tbats | dy.qt | 2018-05-04 | 1440 | 0.0010354 | 0.0010363 | 0.0206722 | 0.1437784 |
| tbats | dy.qt | 2018-05-05 | 1 | 0.0010681 | 0.0010687 | 0.0136020 | 0.1166277 |
| tbats | dy.qt | 2018-05-07 | 1439 | 0.0010949 | 0.0010943 | 0.0214123 | 0.1463294 |
| tbats | dy.qt | 2018-05-08 | 1440 | 0.0008264 | 0.0008266 | 0.0120175 | 0.1096243 |
| tbats | dy.qt | 2018-05-09 | 1440 | 0.0041053 | 0.0040954 | 0.2378058 | 0.4876534 |
| tbats | dy.qt | 2018-05-10 | 1440 | 0.0013572 | 0.0013584 | 0.0376933 | 0.1941477 |
| tbats | dy.qt | 2018-05-11 | 1440 | 0.0007071 | 0.0007073 | 0.0085429 | 0.0924277 |
| tbats | dy.qt | 2018-05-12 | 1 | 0.0001085 | 0.0001085 | 0.0001408 | 0.0118658 |
| tbats | dy.qt | 2018-05-14 | 1439 | 0.0011015 | 0.0011008 | 0.0199788 | 0.1413464 |
| tbats | dy.qt | 2018-05-15 | 1440 | 0.0030341 | 0.0030269 | 0.1740472 | 0.4171897 |
| tbats | dy.qt | 2018-05-16 | 1440 | 0.0010763 | 0.0010771 | 0.0198791 | 0.1409933 |
| tbats | dy.qt | 2018-05-17 | 1440 | 0.0020281 | 0.0020259 | 0.0650995 | 0.2551460 |
| tbats | dy.qt | 2018-05-18 | 1440 | 0.0011063 | 0.0011057 | 0.0197986 | 0.1407074 |
| tbats | dy.qt | 2018-05-19 | 1 | 0.0001151 | 0.0001151 | 0.0001625 | 0.0127482 |
| tbats | dy.qt | 2018-05-21 | 1439 | 0.0034661 | 0.0034591 | 0.1709283 | 0.4134347 |
| tbats | dy.qt | 2018-05-22 | 1440 | 0.0008708 | 0.0008712 | 0.0117005 | 0.1081689 |
| tbats | dy.qt | 2018-05-23 | 1440 | 0.0057107 | 0.0057324 | 0.5328135 | 0.7299408 |
| tbats | dy.qt | 2018-05-24 | 1440 | 0.0049709 | 0.0049858 | 0.3584635 | 0.5987182 |
| tbats | dy.qt | 2018-05-25 | 1440 | 0.0016291 | 0.0016273 | 0.0430735 | 0.2075415 |
| tbats | dy.qt | 2018-05-26 | 1 | 0.0012189 | 0.0012181 | 0.0177330 | 0.1331653 |
| tbats | dy.qt | 2018-05-28 | 1439 | 0.0008189 | 0.0008182 | 0.0181025 | 0.1345455 |
| tbats | dy.qt | 2018-05-29 | 1440 | 0.0046705 | 0.0046848 | 0.3398971 | 0.5830070 |
| tbats | dy.qt | 2018-05-30 | 1440 | 0.0013349 | 0.0013351 | 0.0273525 | 0.1653860 |
| tbats | dy.qt | 2018-05-31 | 1440 | 0.0015381 | 0.0015397 | 0.0399489 | 0.1998722 |
| tbats | dy.qt | 2018-06-01 | 1440 | 0.0039078 | 0.0038975 | 0.2453799 | 0.4953583 |
| tbats | dy.qt | 2018-06-02 | 1 | 0.0064259 | 0.0064053 | 0.4889655 | 0.6992607 |
| tbats | dy.qt | 2018-06-04 | 1439 | 0.0009630 | 0.0009623 | 0.0173505 | 0.1317215 |
| tbats | dy.qt | 2018-06-05 | 1440 | 0.0006841 | 0.0006843 | 0.0091039 | 0.0954142 |
| tbats | dy.qt | 2018-06-06 | 1440 | 0.0020115 | 0.0020087 | 0.0660523 | 0.2570064 |
| tbats | dy.qt | 2018-06-07 | 1440 | 0.0020819 | 0.0020849 | 0.0739407 | 0.2719204 |
| tbats | dy.qt | 2018-06-08 | 1440 | 0.0016482 | 0.0016502 | 0.0492317 | 0.2218821 |
| tbats | dy.qt | 2018-06-09 | 1 | 0.0015419 | 0.0015431 | 0.0286111 | 0.1691482 |
| tbats | dy.qt | 2018-06-11 | 1439 | 0.0031046 | 0.0030989 | 0.1424658 | 0.3774465 |
| tbats | dy.qt | 2018-06-12 | 1440 | 0.0022461 | 0.0022432 | 0.0699830 | 0.2645429 |
| tbats | dy.qt | 2018-06-13 | 1440 | 0.0013507 | 0.0013493 | 0.0326393 | 0.1806636 |
| tbats | dy.qt | 2018-06-14 | 1440 | 0.0017004 | 0.0017015 | 0.0502469 | 0.2241582 |
| tbats | dy.qt | 2018-06-15 | 1440 | 0.0007257 | 0.0007257 | 0.0098517 | 0.0992559 |
| tbats | dy.qt | 2018-06-16 | 1 | 0.0003011 | 0.0003011 | 0.0011100 | 0.0333167 |
| tbats | dy.qt | 2018-06-18 | 1439 | 0.0014155 | 0.0014167 | 0.0292128 | 0.1709174 |
| tbats | dy.qt | 2018-06-19 | 1440 | 0.0052962 | 0.0053126 | 0.4011633 | 0.6333746 |
| tbats | dy.qt | 2018-06-20 | 1440 | 0.0009143 | 0.0009136 | 0.0188498 | 0.1372944 |
| tbats | dy.qt | 2018-06-21 | 1440 | 0.0019756 | 0.0019765 | 0.0688398 | 0.2623733 |
| tbats | dy.qt | 2018-06-22 | 1440 | 0.0006666 | 0.0006664 | 0.0087973 | 0.0937939 |
| tbats | dy.qt | 2018-06-23 | 1 | 0.0000166 | 0.0000166 | 0.0000034 | 0.0018304 |
| tbats | dy.qt | 2018-06-25 | 1439 | 0.0035492 | 0.0035565 | 0.1753105 | 0.4187009 |
| tbats | dy.qt | 2018-06-26 | 1440 | 0.0016580 | 0.0016579 | 0.0462228 | 0.2149950 |
| tbats | dy.qt | 2018-06-27 | 1440 | 0.0016472 | 0.0016466 | 0.0434048 | 0.2083381 |
| tbats | dy.qt | 2018-06-28 | 1440 | 0.0008681 | 0.0008678 | 0.0167567 | 0.1294476 |
| tbats | dy.qt | 2018-06-29 | 1440 | 0.0015291 | 0.0015275 | 0.0394970 | 0.1987385 |
| tbats | dy.qt | 2018-06-30 | 1 | 0.0017288 | 0.0017273 | 0.0364923 | 0.1910297 |
| tbats | dy.qt | 2018-07-02 | 1439 | 0.0010487 | 0.0010478 | 0.0211690 | 0.1454958 |
| tbats | dy.qt | 2018-07-03 | 1440 | 0.0012694 | 0.0012706 | 0.0347796 | 0.1864930 |
| tbats | dy.qt | 2018-07-04 | 1440 | 0.0010272 | 0.0010279 | 0.0163587 | 0.1279010 |
| tbats | dy.qt | 2018-07-05 | 1440 | 0.0009826 | 0.0009822 | 0.0142237 | 0.1192630 |
| tbats | dy.qt | 2018-07-06 | 1440 | 0.0008012 | 0.0008016 | 0.0131406 | 0.1146326 |
| tbats | dy.qt | 2018-07-07 | 1 | 0.0016441 | 0.0016454 | 0.0330902 | 0.1819072 |
| tbats | dy.yr | 2018-01-03 | 1439 | 0.0031414 | 0.0031467 | 0.1318562 | 0.3631201 |
| tbats | dy.yr | 2018-01-04 | 1440 | 0.0007263 | 0.0007263 | 0.0088109 | 0.0938664 |
| tbats | dy.yr | 2018-01-05 | 1440 | 0.0033109 | 0.0033042 | 0.1712639 | 0.4138404 |
| tbats | dy.yr | 2018-01-06 | 1 | 0.0033901 | 0.0033844 | 0.1459240 | 0.3820000 |
| tbats | dy.yr | 2018-01-08 | 1439 | 0.0039391 | 0.0039311 | 0.2050746 | 0.4528517 |
| tbats | dy.yr | 2018-01-09 | 1440 | 0.0012943 | 0.0012931 | 0.0419181 | 0.2047390 |
| tbats | dy.yr | 2018-01-10 | 1440 | 0.0073048 | 0.0073400 | 0.8879488 | 0.9423103 |
| tbats | dy.yr | 2018-01-11 | 1440 | 0.0103775 | 0.0104334 | 1.4110712 | 1.1878852 |
| tbats | dy.yr | 2018-01-12 | 1440 | 0.0130046 | 0.0130904 | 2.1649021 | 1.4713606 |
| tbats | dy.yr | 2018-01-13 | 1 | 0.0147054 | 0.0148143 | 2.7456490 | 1.6570000 |
| tbats | dy.yr | 2018-01-15 | 1439 | 0.0177735 | 0.0179342 | 4.0444477 | 2.0110812 |
| tbats | dy.yr | 2018-01-16 | 1440 | 0.0175204 | 0.0176763 | 3.9235329 | 1.9807910 |
| tbats | dy.yr | 2018-01-17 | 1440 | 0.0173391 | 0.0174925 | 3.8604893 | 1.9648128 |
| tbats | dy.yr | 2018-01-18 | 1440 | 0.0132828 | 0.0133725 | 2.2636575 | 1.5045456 |
| tbats | dy.yr | 2018-01-19 | 1440 | 0.0169647 | 0.0171110 | 3.6821392 | 1.9188901 |
| tbats | dy.yr | 2018-01-20 | 1 | 0.0163738 | 0.0165090 | 3.4040250 | 1.8450000 |
| tbats | dy.yr | 2018-01-22 | 1439 | 0.0164475 | 0.0165846 | 3.4523110 | 1.8580396 |
| tbats | dy.yr | 2018-01-23 | 1440 | 0.0180156 | 0.0181820 | 4.1856644 | 2.0458896 |
| tbats | dy.yr | 2018-01-24 | 1440 | 0.0268881 | 0.0272614 | 9.3470597 | 3.0572961 |
| tbats | dy.yr | 2018-01-25 | 1440 | 0.0322722 | 0.0328036 | 13.2754674 | 3.6435515 |
| tbats | dy.yr | 2018-01-26 | 1440 | 0.0318377 | 0.0323591 | 13.0263583 | 3.6092047 |
| tbats | dy.yr | 2018-01-27 | 1 | 0.0359514 | 0.0366094 | 16.4106010 | 4.0510000 |
| tbats | dy.yr | 2018-01-29 | 1439 | 0.0339983 | 0.0345871 | 14.6966838 | 3.8336254 |
| tbats | dy.yr | 2018-01-30 | 1440 | 0.0346458 | 0.0352574 | 15.2604667 | 3.9064647 |
| tbats | dy.yr | 2018-01-31 | 1440 | 0.0333584 | 0.0339260 | 14.1707246 | 3.7644023 |
| tbats | dy.yr | 2018-02-01 | 1440 | 0.0288410 | 0.0292640 | 10.5843271 | 3.2533563 |
| tbats | dy.yr | 2018-02-02 | 1440 | 0.0249175 | 0.0252362 | 7.9895620 | 2.8265813 |
| tbats | dy.yr | 2018-02-03 | 1 | 0.0222400 | 0.0224901 | 6.2800360 | 2.5060000 |
| tbats | dy.yr | 2018-02-05 | 1439 | 0.0247250 | 0.0250364 | 7.8101566 | 2.7946657 |
| tbats | dy.yr | 2018-02-06 | 1440 | 0.0316136 | 0.0321241 | 12.7564999 | 3.5716243 |
| tbats | dy.yr | 2018-02-07 | 1440 | 0.0298147 | 0.0302673 | 11.3204578 | 3.3645888 |
| tbats | dy.yr | 2018-02-08 | 1440 | 0.0295570 | 0.0300045 | 11.1915858 | 3.3453828 |
| tbats | dy.yr | 2018-02-09 | 1440 | 0.0340752 | 0.0346683 | 14.8008132 | 3.8471825 |
| tbats | dy.yr | 2018-02-10 | 1 | 0.0344693 | 0.0350738 | 15.0854560 | 3.8840000 |
| tbats | dy.yr | 2018-02-12 | 1439 | 0.0355512 | 0.0361948 | 16.0525253 | 4.0065603 |
| tbats | dy.yr | 2018-02-13 | 1440 | 0.0415012 | 0.0423895 | 22.0797777 | 4.6989124 |
| tbats | dy.yr | 2018-02-14 | 1440 | 0.0478455 | 0.0490216 | 29.1477209 | 5.3988629 |
| tbats | dy.yr | 2018-02-15 | 1440 | 0.0548283 | 0.0563755 | 38.2107906 | 6.1814877 |
| tbats | dy.yr | 2018-02-16 | 1440 | 0.0585071 | 0.0602717 | 43.4960112 | 6.5951506 |
| tbats | dy.yr | 2018-02-17 | 1 | 0.0565673 | 0.0582138 | 40.6278760 | 6.3740000 |
| tbats | dy.yr | 2018-02-19 | 1439 | 0.0550766 | 0.0566373 | 38.5369395 | 6.2078128 |
| tbats | dy.yr | 2018-02-20 | 1440 | 0.0503269 | 0.0516282 | 32.2105882 | 5.6754373 |
| tbats | dy.yr | 2018-02-21 | 1440 | 0.0451023 | 0.0461438 | 25.8503062 | 5.0843196 |
| tbats | dy.yr | 2018-02-22 | 1440 | 0.0486687 | 0.0498868 | 30.1747998 | 5.4931594 |
| tbats | dy.yr | 2018-02-23 | 1440 | 0.0520678 | 0.0534602 | 34.4368323 | 5.8682904 |
| tbats | dy.yr | 2018-02-24 | 1 | 0.0513756 | 0.0527301 | 33.5125210 | 5.7890000 |
| tbats | dy.yr | 2018-02-26 | 1439 | 0.0523297 | 0.0537373 | 34.8061849 | 5.8996767 |
| tbats | dy.yr | 2018-02-27 | 1440 | 0.0495722 | 0.0508339 | 31.2421536 | 5.5894681 |
| tbats | dy.yr | 2018-02-28 | 1440 | 0.0500147 | 0.0512998 | 31.8154528 | 5.6405188 |
| tbats | dy.yr | 2018-03-01 | 1440 | 0.0528801 | 0.0543178 | 35.5425360 | 5.9617561 |
| tbats | dy.yr | 2018-03-02 | 1440 | 0.0614139 | 0.0633632 | 47.9736591 | 6.9263020 |
| tbats | dy.yr | 2018-03-03 | 1 | 0.0617146 | 0.0636796 | 48.3581160 | 6.9540000 |
| tbats | dy.yr | 2018-03-05 | 1439 | 0.0618393 | 0.0638152 | 48.6191767 | 6.9727453 |
| tbats | dy.yr | 2018-03-06 | 1440 | 0.0576352 | 0.0593462 | 42.1946350 | 6.4957398 |
| tbats | dy.yr | 2018-03-07 | 1440 | 0.0611436 | 0.0630732 | 47.4988149 | 6.8919384 |
| tbats | dy.yr | 2018-03-08 | 1440 | 0.0583970 | 0.0601537 | 43.3046139 | 6.5806241 |
| tbats | dy.yr | 2018-03-09 | 1440 | 0.0528147 | 0.0542485 | 35.4452447 | 5.9535909 |
| tbats | dy.yr | 2018-03-10 | 1 | 0.0519302 | 0.0533146 | 34.2400523 | 5.8515000 |
| tbats | dy.yr | 2018-03-12 | 1439 | 0.0539580 | 0.0554551 | 36.9899617 | 6.0819373 |
| tbats | dy.yr | 2018-03-13 | 1440 | 0.0530344 | 0.0544823 | 35.7881548 | 5.9823202 |
| tbats | dy.yr | 2018-03-14 | 1440 | 0.0552759 | 0.0568478 | 38.8117093 | 6.2299044 |
| tbats | dy.yr | 2018-03-15 | 1440 | 0.0586386 | 0.0604106 | 43.6777665 | 6.6089157 |
| tbats | dy.yr | 2018-03-16 | 1440 | 0.0593666 | 0.0611845 | 44.7900387 | 6.6925360 |
| tbats | dy.yr | 2018-03-17 | 1 | 0.0594382 | 0.0612588 | 44.8565063 | 6.6975000 |
| tbats | dy.yr | 2018-03-19 | 1439 | 0.0596944 | 0.0615318 | 45.2649130 | 6.7279204 |
| tbats | dy.yr | 2018-03-20 | 1440 | 0.0564654 | 0.0581070 | 40.5082290 | 6.3646075 |
| tbats | dy.yr | 2018-03-21 | 1440 | 0.0561626 | 0.0577863 | 40.0706968 | 6.3301419 |
| tbats | dy.yr | 2018-03-22 | 1440 | 0.0620814 | 0.0640717 | 48.9713686 | 6.9979546 |
| tbats | dy.yr | 2018-03-23 | 1440 | 0.0686503 | 0.0710915 | 59.8598804 | 7.7369167 |
| tbats | dy.yr | 2018-03-24 | 1 | 0.0705005 | 0.0730765 | 63.1071360 | 7.9440000 |
| tbats | dy.yr | 2018-03-26 | 1439 | 0.0678501 | 0.0702341 | 58.4820533 | 7.6473560 |
| tbats | dy.yr | 2018-03-27 | 1440 | 0.0627230 | 0.0647543 | 49.9636189 | 7.0684948 |
| tbats | dy.yr | 2018-03-28 | 1440 | 0.0600072 | 0.0618740 | 45.9681799 | 6.7799838 |
| tbats | dy.yr | 2018-03-29 | 1440 | 0.0542516 | 0.0557653 | 37.3936332 | 6.1150334 |
| tbats | dy.yr | 2018-03-30 | 1440 | 0.0569742 | 0.0586453 | 41.2251844 | 6.4206841 |
| tbats | dy.yr | 2018-03-31 | 1 | 0.0567403 | 0.0583971 | 40.8768423 | 6.3935000 |
| tbats | dy.yr | 2018-04-02 | 1439 | 0.0573346 | 0.0590282 | 41.7708572 | 6.4630378 |
| tbats | dy.yr | 2018-04-03 | 1440 | 0.0578294 | 0.0595547 | 42.5392525 | 6.5222122 |
| tbats | dy.yr | 2018-04-04 | 1440 | 0.0551418 | 0.0567069 | 38.6452777 | 6.2165326 |
| tbats | dy.yr | 2018-04-05 | 1440 | 0.0496996 | 0.0509684 | 31.4156586 | 5.6049673 |
| tbats | dy.yr | 2018-04-06 | 1440 | 0.0486093 | 0.0498215 | 30.0316667 | 5.4801156 |
| tbats | dy.yr | 2018-04-07 | 1 | 0.0509585 | 0.0522908 | 32.9705640 | 5.7420000 |
| tbats | dy.yr | 2018-04-09 | 1439 | 0.0505655 | 0.0518776 | 32.4760320 | 5.6987746 |
| tbats | dy.yr | 2018-04-10 | 1440 | 0.0500467 | 0.0513325 | 31.8318784 | 5.6419747 |
| tbats | dy.yr | 2018-04-11 | 1440 | 0.0505795 | 0.0518926 | 32.5015772 | 5.7010155 |
| tbats | dy.yr | 2018-04-12 | 1440 | 0.0500981 | 0.0513869 | 31.9055113 | 5.6484964 |
| tbats | dy.yr | 2018-04-13 | 1440 | 0.0462221 | 0.0473164 | 27.1456958 | 5.2101531 |
| tbats | dy.yr | 2018-04-14 | 1 | 0.0472533 | 0.0483967 | 28.3503003 | 5.3245000 |
| tbats | dy.yr | 2018-04-16 | 1439 | 0.0480113 | 0.0491929 | 29.2834761 | 5.4114209 |
| tbats | dy.yr | 2018-04-17 | 1440 | 0.0499536 | 0.0512334 | 31.6868643 | 5.6291087 |
| tbats | dy.yr | 2018-04-18 | 1440 | 0.0484214 | 0.0496232 | 29.7780866 | 5.4569301 |
| tbats | dy.yr | 2018-04-19 | 1440 | 0.0471391 | 0.0482772 | 28.2180613 | 5.3120675 |
| tbats | dy.yr | 2018-04-20 | 1440 | 0.0451939 | 0.0462391 | 25.9423588 | 5.0933642 |
| tbats | dy.yr | 2018-04-21 | 1 | 0.0447107 | 0.0457331 | 25.3814440 | 5.0380000 |
| tbats | dy.yr | 2018-04-23 | 1439 | 0.0403732 | 0.0412102 | 20.8190835 | 4.5627934 |
| tbats | dy.yr | 2018-04-24 | 1440 | 0.0342189 | 0.0348152 | 14.8829677 | 3.8578450 |
| tbats | dy.yr | 2018-04-25 | 1440 | 0.0316863 | 0.0321978 | 12.7813704 | 3.5751042 |
| tbats | dy.yr | 2018-04-26 | 1440 | 0.0298544 | 0.0303070 | 11.3227741 | 3.3649330 |
| tbats | dy.yr | 2018-04-27 | 1440 | 0.0305881 | 0.0310636 | 11.8910975 | 3.4483471 |
| tbats | dy.yr | 2018-04-28 | 1 | 0.0321441 | 0.0326692 | 13.1188840 | 3.6220000 |
| tbats | dy.yr | 2018-04-30 | 1439 | 0.0306979 | 0.0311769 | 11.9756958 | 3.4605918 |
| tbats | dy.yr | 2018-05-01 | 1440 | 0.0279642 | 0.0283622 | 9.9632937 | 3.1564685 |
| tbats | dy.yr | 2018-05-02 | 1440 | 0.0253920 | 0.0257187 | 8.1921161 | 2.8621873 |
| tbats | dy.yr | 2018-05-03 | 1440 | 0.0283529 | 0.0287634 | 10.2724713 | 3.2050696 |
| tbats | dy.yr | 2018-05-04 | 1440 | 0.0319213 | 0.0324394 | 12.9459186 | 3.5980437 |
| tbats | dy.yr | 2018-05-05 | 1 | 0.0319799 | 0.0324996 | 12.9852123 | 3.6035000 |
| tbats | dy.yr | 2018-05-07 | 1439 | 0.0314228 | 0.0319251 | 12.5540949 | 3.5431758 |
| tbats | dy.yr | 2018-05-08 | 1440 | 0.0322355 | 0.0327640 | 13.2033796 | 3.6336455 |
| tbats | dy.yr | 2018-05-09 | 1440 | 0.0276971 | 0.0280882 | 9.7920757 | 3.1292292 |
| tbats | dy.yr | 2018-05-10 | 1440 | 0.0268879 | 0.0272554 | 9.2076423 | 3.0344097 |
| tbats | dy.yr | 2018-05-11 | 1440 | 0.0295278 | 0.0299706 | 11.0766470 | 3.3281597 |
| tbats | dy.yr | 2018-05-12 | 1 | 0.0292332 | 0.0296669 | 10.8504360 | 3.2940000 |
| tbats | dy.yr | 2018-05-14 | 1439 | 0.0285502 | 0.0289643 | 10.3633711 | 3.2192190 |
| tbats | dy.yr | 2018-05-15 | 1440 | 0.0238221 | 0.0241119 | 7.2687680 | 2.6960653 |
| tbats | dy.yr | 2018-05-16 | 1440 | 0.0217231 | 0.0219618 | 5.9972995 | 2.4489384 |
| tbats | dy.yr | 2018-05-17 | 1440 | 0.0190188 | 0.0192032 | 4.6376754 | 2.1535263 |
| tbats | dy.yr | 2018-05-18 | 1440 | 0.0162332 | 0.0163665 | 3.3582588 | 1.8325553 |
| tbats | dy.yr | 2018-05-19 | 1 | 0.0171015 | 0.0172490 | 3.7133290 | 1.9270000 |
| tbats | dy.yr | 2018-05-21 | 1439 | 0.0136949 | 0.0137903 | 2.4048528 | 1.5507588 |
| tbats | dy.yr | 2018-05-22 | 1440 | 0.0152313 | 0.0153483 | 2.9492781 | 1.7173462 |
| tbats | dy.yr | 2018-05-23 | 1440 | 0.0214290 | 0.0216665 | 5.9628655 | 2.4418979 |
| tbats | dy.yr | 2018-05-24 | 1440 | 0.0278934 | 0.0282903 | 9.9377873 | 3.1524256 |
| tbats | dy.yr | 2018-05-25 | 1440 | 0.0289092 | 0.0293338 | 10.6257407 | 3.2597148 |
| tbats | dy.yr | 2018-05-26 | 1 | 0.0292155 | 0.0296486 | 10.8372640 | 3.2920000 |
| tbats | dy.yr | 2018-05-28 | 1439 | 0.0287038 | 0.0291224 | 10.4758182 | 3.2366369 |
| tbats | dy.yr | 2018-05-29 | 1440 | 0.0334591 | 0.0340318 | 14.2958765 | 3.7809888 |
| tbats | dy.yr | 2018-05-30 | 1440 | 0.0348500 | 0.0354691 | 15.4474376 | 3.9303228 |
| tbats | dy.yr | 2018-05-31 | 1440 | 0.0349467 | 0.0355687 | 15.5187281 | 3.9393817 |
| tbats | dy.yr | 2018-06-01 | 1440 | 0.0305646 | 0.0310420 | 11.9334252 | 3.4544790 |
| tbats | dy.yr | 2018-06-02 | 1 | 0.0280529 | 0.0284520 | 9.9919210 | 3.1610000 |
| tbats | dy.yr | 2018-06-04 | 1439 | 0.0272565 | 0.0276335 | 9.4419288 | 3.0727722 |
| tbats | dy.yr | 2018-06-05 | 1440 | 0.0256171 | 0.0259498 | 8.3406851 | 2.8880244 |
| tbats | dy.yr | 2018-06-06 | 1440 | 0.0236709 | 0.0239552 | 7.1314719 | 2.6704816 |
| tbats | dy.yr | 2018-06-07 | 1440 | 0.0241939 | 0.0244910 | 7.4534678 | 2.7301040 |
| tbats | dy.yr | 2018-06-08 | 1440 | 0.0278386 | 0.0282325 | 9.8637981 | 3.1406684 |
| tbats | dy.yr | 2018-06-09 | 1 | 0.0279331 | 0.0283287 | 9.9067563 | 3.1475000 |
| tbats | dy.yr | 2018-06-11 | 1439 | 0.0253705 | 0.0256989 | 8.2308141 | 2.8689395 |
| tbats | dy.yr | 2018-06-12 | 1440 | 0.0213017 | 0.0215314 | 5.7706147 | 2.4022104 |
| tbats | dy.yr | 2018-06-13 | 1440 | 0.0191762 | 0.0193623 | 4.6803909 | 2.1634211 |
| tbats | dy.yr | 2018-06-14 | 1440 | 0.0215490 | 0.0217855 | 5.9378640 | 2.4367733 |
| tbats | dy.yr | 2018-06-15 | 1440 | 0.0182994 | 0.0184688 | 4.2613323 | 2.0642995 |
| tbats | dy.yr | 2018-06-16 | 1 | 0.0178781 | 0.0180393 | 4.0582102 | 2.0145000 |
| tbats | dy.yr | 2018-06-18 | 1439 | 0.0192425 | 0.0194297 | 4.7069267 | 2.1695453 |
| tbats | dy.yr | 2018-06-19 | 1440 | 0.0241006 | 0.0243970 | 7.4340138 | 2.7265388 |
| tbats | dy.yr | 2018-06-20 | 1440 | 0.0224995 | 0.0227559 | 6.4389355 | 2.5375058 |
| tbats | dy.yr | 2018-06-21 | 1440 | 0.0208018 | 0.0210232 | 5.5623215 | 2.3584574 |
| tbats | dy.yr | 2018-06-22 | 1440 | 0.0236769 | 0.0239609 | 7.1257653 | 2.6694129 |
| tbats | dy.yr | 2018-06-23 | 1 | 0.0238995 | 0.0241886 | 7.2522490 | 2.6930000 |
| tbats | dy.yr | 2018-06-25 | 1439 | 0.0273632 | 0.0277437 | 9.5296900 | 3.0870196 |
| tbats | dy.yr | 2018-06-26 | 1440 | 0.0261115 | 0.0264588 | 8.7023493 | 2.9499745 |
| tbats | dy.yr | 2018-06-27 | 1440 | 0.0231693 | 0.0234426 | 6.8580605 | 2.6187899 |
| tbats | dy.yr | 2018-06-28 | 1440 | 0.0212360 | 0.0214646 | 5.7420078 | 2.3962487 |
| tbats | dy.yr | 2018-06-29 | 1440 | 0.0179686 | 0.0181321 | 4.1138114 | 2.0282533 |
| tbats | dy.yr | 2018-06-30 | 1 | 0.0176784 | 0.0178360 | 3.9680640 | 1.9920000 |
| tbats | dy.yr | 2018-07-02 | 1439 | 0.0166676 | 0.0168080 | 3.5355166 | 1.8802969 |
| tbats | dy.yr | 2018-07-03 | 1440 | 0.0167358 | 0.0168780 | 3.5806198 | 1.8922526 |
| tbats | dy.yr | 2018-07-04 | 1440 | 0.0196316 | 0.0198264 | 4.8968547 | 2.2128838 |
| tbats | dy.yr | 2018-07-05 | 1440 | 0.0009931 | 0.0009929 | 0.0174183 | 0.1319785 |
| tbats | dy.yr | 2018-07-06 | 1440 | 0.0007986 | 0.0007990 | 0.0130234 | 0.1141202 |
| tbats | dy.yr | 2018-07-07 | 1 | 0.0016348 | 0.0016361 | 0.0327167 | 0.1808775 |
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p1 <- yr_2018 %>%
ggplot(aes(x = index, y = open, group = Model, color = Model)) +
geom_line() +
#scale_colour_gradient2_tableau(palette = names(palettes)[1]) + #first palettes list in name
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Open Price Forecasting',
subtitle = paste('From', range(unique(yr_2018$index))[1L], 'to', range(unique(yr_2018$index))[2L]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
##scale_fill_manual(values = tableau_colours) +
#scale_color_brewer(tableau_colours) +
#scale_color_jcolors(palette = palettes2$`Tableau 20`$value) + #choose color set among palettes
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
## Due to heavily loading in plotly graph, here I use ggplot.
#ply1 <- ggplotly(p1)
#ply1
p1
7.1.3.0.2 High Price
rm(p1)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p2 <- yr_2018 %>%
ggplot(aes(x = index, y = high, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min High Price Forecasting',
subtitle = paste('From', range(unique(yr_2018$index))[1L], 'to', range(unique(yr_2018$index))[2L]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
## Due to heavily loading in plotly graph, here I use ggplot.
#ply2 <- ggplotly(p2)
#ply2
p2
7.1.3.0.3 Low Price
rm(p2)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p3 <- yr_2018 %>%
ggplot(aes(x = index, y = low, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Low Price Forecasting',
subtitle = paste('From', range(unique(yr_2018$index))[1], 'to', range(unique(yr_2018$index))[2]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
## Due to heavily loading in plotly graph, here I use ggplot.
#ply3 <- ggplotly(p3)
#ply3
p3
7.1.3.0.4 Close Price
rm(p3)
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p4 <- yr_2018 %>%
ggplot(aes(x = index, y = close, group = Model, color = Model)) +
geom_line() +
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Close Price Forecasting',
subtitle = paste('From', range(unique(yr_2018$index))[1], 'to', range(unique(yr_2018$index))[2]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
## Due to heavily loading in plotly graph, here I use ggplot.
#ply4 <- ggplotly(p4)
#ply4
p4
## https://www.r-graph-gallery.com/line-chart-several-groups-ggplot2.html
p5 <- mDT %>%
ggplot(aes(x = index, y = Price, group = Model, color = Model)) +
geom_line() +
#scale_colour_gradient2_tableau(palette = names(palettes)[1]) + #first palettes list in name
#scale_color_viridis(discrete = TRUE) +
labs(title = '1 min Open Price Forecasting',
subtitle = paste('From', range(unique(mDT$index))[1L], 'to', range(unique(mDT$index))[2L]),
caption = "Data source: fxcm") +
ylab('Exchange Rates USD/JPY') +
theme_economist() +
#scale_color_economist() +
##scale_fill_manual(values = tableau_colours) +
#scale_color_brewer(tableau_colours) +
#scale_color_jcolors(palette = palettes2$`Tableau 20`$value) + #choose color set among palettes
#theme(axis.text.x = element_text(hjust = c(0, 0.5, 0.5, 0.5, 1))) +
theme(legend.position = 'right')
## Due to heavily loading in plotly graph, here I use ggplot.
#ply5 <- ggplotly(p5)
#ply5
p5
Kindly refer to Traceback-HFT.R for more information. Here I tried to recalculate dataset from year 2018-01-01 to 2018-07-09 but the outcome is same. Here I forced to omit the mentioned dataset.
## ------------ eval = FALSE -------------------
## Due to high volume dataset and heavily ploting, here I ommit it.
yr_2018 %>%
group_by(Model) %>%
e_charts(x = index) %>%
e_line(open.Point.Forecast, smooth = TRUE) %>%
e_datazoom(
type = 'slider',
toolbox = FALSE,
bottom = -5) %>%
e_tooltip() %>%
e_title(text = 'Model', subtext = 'open.Point.Forecast', left = 'center') %>%
e_axis_labels(x = 'index', y = 'open.Point.Forecast') %>%
e_x_axis(index, axisPointer = list(show = TRUE)) %>%
e_legend(
orient = 'vertical',
type = c('scroll'),
#selectedMode = 'multiple', #https://echarts.apache.org/en/option.html#legend
#selected = list('Model'),
left = 0, top = 80) %>%
e_grid(left = 150, top = 90) %>%
#e_theme('shine') %>%
e_toolbox_feature('saveAsImage', title = 'Screenshot')7.2 Documenting File Creation
It’s useful to record some information about how your file was created.
- File creation date: 2018-08-28
- File latest updated date: 2021-01-22
- R version 4.0.3 (2020-10-10)
- R version (short form): 4.0.3
- rmarkdown package version: 2.6
- File version: 1.0.1
- Author Profile: ®γσ, Eng Lian Hu
- GitHub: Source Code
- Additional session information:
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('magrittr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))
suppressMessages(require('knitr', quietly = TRUE))
suppressMessages(require('kableExtra', quietly = TRUE))
sys1 <- devtools::session_info()$platform %>%
unlist %>% data.frame(Category = names(.), session_info = .)
rownames(sys1) <- NULL
sys2 <- data.frame(Sys.info()) %>%
mutate(Category = rownames(.)) %>% .[2:1]
names(sys2)[2] <- c('Sys.info')
rownames(sys2) <- NULL
if (nrow(sys1) == 9 & nrow(sys2) == 8) {
sys2 %<>% rbind(., data.frame(
Category = 'Current time',
Sys.info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
} else {
sys1 %<>% rbind(., data.frame(
Category = 'Current time',
session_info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
}
cbind(sys1, sys2) %>%
kbl(caption = 'Additional session information:') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
row_spec(0, background = 'DimGrey') %>%
row_spec(9, bold = T, color = 'white', background = '#D7261E')| Category | session_info | Category | Sys.info |
|---|---|---|---|
| version | R version 4.0.3 (2020-10-10) | sysname | Windows |
| os | Windows 10 x64 | release | 10 x64 |
| system | x86_64, mingw32 | version | build 19042 |
| ui | RTerm | nodename | SCIBROKES-TRADI |
| language | en | machine | x86-64 |
| collate | English_World.1252 | login | Owner |
| ctype | English_World.1252 | user | Owner |
| tz | Asia/Tokyo | effective_user | Owner |
| date | 2021-01-22 | Current time | 2021-01-22 06:13:14 JST<U+0001F5FE> |
7.3 Reference
- Mixed Frequency Data Sampling Regression Models - The R Package midasr
- binary.com Interview Question I - Comparison of Univariate GARCH Models
- GARCH模型中的ARIMA(p,d,q)参数最优化
- Forecasting the Return Volatility of Energy Prices - A GARCH-MIDAS Approach
- Levy Processes For Finance - An Intrudction in R
- MIDAS Regressions - Further Results and New Directions
- High- and Low-Frequency Correlations in European Government Bond Spreads and Their Macroeconomic Drivers
- FracSim - An R Package to Simulate Multifractional Levy Motions
- Volatility Models and Their Applications
- Using Midas to estimate a Garch-Midas model
- A Comparison of GARCH-class Models and MIDAS Regression with Application in Volatility Prediction and Value at Risk Estimation
- Importance of the Macroeconomic Variables for Variance Prediction - A GARCH-MIDAS Approach
- Mixed Frequency Data Sampling Regression Models - The R Package midasr (paper)
- Forecasting with
midasrpackage: Inclusion of new high-frequency value - Handbook of Volatility Models and Their Applications
- High Frequency Financial Time Series Prediction - Machine Learning Approach
- High Frequency GARCH: The multiplicative component GARCH (mcsGARCH) model
- A Review of Literature on Time Zone Difference and Trade
- binary.com Interview Question I - Tick-Data-HiLo For Daily Trading (Blooper)
- Forecasting: Principles and Practice
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Sςιβrοκεrs Trαdιηg®️経営企業
For buying order, we need to refer to
askprice and selling order need to refer tobidprice.↩︎Seasonal periods describe very details on the
seasonal periodparameters determination.↩︎help of
auto.arima()describe theseasonal : If FALSE, restricts search to non-seasonal models.↩︎